Table of Contents · Age Computation 04 Boys’ CDC Height Tables 05 Boys’ CDC Mass Tables 08...

Detailed Calculations of M. E.’s Growth-and-Obesity Vector-Roadmap

Possible Validation of Mathematical Definition of Childhood Obesity based on Anthropome- tric Data Collected during 1998-2013

Additional File 1

SYED ARIF KAMAL

ASHFAQ ALI NAZ

SHAKEEL AHMED ANSARI

POSSIBLE VALIDATION OF MATHEMATICAL DEFINITION OF

CHILDHOOD OBESITY BASED ON ANTHROPOMETRIC

DATA COLLECTED DURING 1998-2013

https://www.ngds-ku.org/Papers/J46.pdf

Syed Arif Kamal*, Ashfaq Ali. Naz and Shakeel Ahmed Ansari

Additional File 3

*Homepage: https://www.ngds-ku.org/kamal • project URL: https://ngds-ku.org • e-mail: [email protected]

COPYRIGHT 2017. THE NGDS PILOT PROJECT, PO BOX 8423, KARACHI 75270, PAKISTAN

1

DETAILED CALCULATIONS OF M. E.’s

GROWTH-AND-OBESITY VECTOR-ROADMAP

Table of Contents

Calculation Sequence 02

Checkup Data 03

Age Computation 04

Boys’ CDC Height Tables 05

Boys’ CDC Mass Tables 08

Girls’ CDC Height Tables 11

Girls’ CDC Mass Tables 16

Evaluation of Height and Mass Percentiles 21

Evaluation of Height-Percentile-based-Optimal Mass, Estimated-Adult Height and Mass 26

Mid-Parental and Army-Cutoff Heights at Current Age 32

Build, Nutritional Status and Reference Percentile 42

Evaluation of BMI-based-Optimal Mass 44

Control-Action Trajectories for Height and Mass Percentiles 49

Height and Mass Recommendations 50

Growth-and-Obesity Vector-Roadmap 56

Color Scheme of Growth-and-Obesity Vector-Roadmap 58

References 61

This file first appeared as Additional File 2

https://www.ngds-ku.org/Papers/J45/Additional_File_2.pdf

of ‘In Search of a Definition of Childhood Obesity’ by Syed Arif Kamal

ADDITIONAL FILE 3: DETAILED CALCULATIONS OF M. E.’S GROWTH-AND-OBESITY VECTOR-ROADMAP


2

Calculation Sequence

Data

Country of Origin

Gender

Date of Birth

Date of Checkup

Height

Mass

Dress Code

Height of Biological Father

Height of Biological Mother

Calculations

Decimal Age

Percentile of Height

Percentile of Mass

Percentile of BMI-based-Optimal Mass

Estimated-Adult Height

Estimated-Adult Mass

Current-Age-Mid-Parental Height

Current-Age-Army-Cutoff Height

Height-Percentile-based-Optimal Mass

BMI-based-Optimal Mass

Results

Algebraic Status (pertaining-to-height)

Algebraic Status (pertaining-to-mass)

Estimated-Adult BMI

Nutritional Status

Build

6-month-Height Management

6-month-Mass Management

SYED ARIF KAMAL, ASHFAQ ALI NAZ AND SHAKEEL AHMED ANSARI


3

Checkup Data

Table AFIII-1. Ages, heights and masses of M. E. (Country of Origin: Pakistan)

Date of BirthɎ

(year-month-day): 2002-09-23 • Date of Birth (decimal years): 2002.728767123287671

___________________________________________________

ɎDates in the format YYYY–MM–DD may be converted to decimal form using the formulae given on page 4 and Table

AFIII-2.

§h (in)

542

)(

.

cm h; 1 ft 12 in; 1 in 2.54 cm — ft stands for foot (feet); in for inch(es); cm for centimeter(s)

¶For explanation of dress code (undressing), see Kamal (2006).

$T-shirt, skirt (Undressing: to panties only, barefoot, all clothing above the waist removed)

@Clothing Correction was taken as zero as the child was weighed in near-nude state

®1 kg 2.205 lb; 1 lb 16 oz

Gender: Female

1st Checkup

2nd

Checkup

Date of Checkup

(year-month-day)

2011-05-22

2011-11-13

Date of Checkup

(decimal years)

2011.389041095890411

2011.8684931506849315

Age (year-month-day)

08-07-29

09-01-20

Age, A (decimal years)

8.6602739726027398 9.1397260273972603

Height, h (cm)

129.50

131.00

Height (ft-in)§

4 ft 2.984251968503937 in 4 ft 3.574803149606299 in

Gross Mass (kg)

31.90 31.79

Dress Code¶

1.5/1.5 (0/0.5)$ 1.5/1.5 (0/0.5)

$

Clothing Correction (kg)@

0

0

Net Mass, (kg)

31.90

31.79

Net Weight, W (lb-oz)®

70 lb 5.432 oz 70 lb 1.5512 oz



4

Age Computation

Non-Leap Year: 365

)()1( DDDaysMMDaysYYYY

Leap Year: 366

)()1( DDDaysMMDaysYYYY

Table AFIII-2. Cumulative days in a year£

# Months Non-leap Year Leap Year

Days Cumulative Days Days Cumulative Days

01 January 31 31 31 131

02 February 28 159 29 60

03 March 31 190 31 191

04 April 30 120 30 121

05 May 31 151 31 152

06 June 30 181 30 182

07 July 31 212 31 213

08 August 31 243 31 244

09 September 30 273 30 274

10 October 31 304 31 305

11 November 30 334 30 335

12 December 31 365 31 366

Date of Birth of M. E. 2002-09-23 2002.7287671232876712

Date of First Checkup 2011-05-22 2011.389041095890411

Date of Second Checkup 2011-11-13 2011.8684931506849315

Age (decimal year)Date of Checkup – Date of Birth

Age at the First Checkup

2011.389041095890411 – 2002.7287671232876712 8.6602739726027398 years

Age at the Second Checkup

2011.8684931506849315 – 2002.7287671232876712 9.1397260273972603 years

____________________________________________

£First appeared as Table 4 on page 94 of Kamal et al. (2011)

365

232432002

365

221202011

365

133042011



5

Boys’ CDC Height Table

Table AFIII-3a. Boys’ heights in centimeters for the percentile range 5-95

Percentiles

Ages (years)

5 10 25 50 75 90 95

2.0 Height 80.729770 81.991710 84.102890 86.452200 88.805250 90.926190 92.196880

2.5 Height 85.008210 86.300625 88.493865 90.980750 93.521075 95.853805 97.271125

3.0 Height 88.894195 90.188025 92.407180 94.959980 97.608725 100.078495 101.596950

3.5 Height 92.234155 93.635200 96.010620 98.700785 101.445200 103.962200 105.490000

4.0 Height 95.329380 96.843585 99.384695 102.223900 105.079500 107.663450 109.216050

4.5 Height 98.295495 99.914900 102.614150 105.603750 108.583650 111.257600 112.854400

5.0 Height 101.209950 102.921750 105.765750 108.902350 112.015700 114.798550 116.455550

5.5 Height 104.125200 105.913250 108.883550 112.159300 115.410250 118.315900 120.045950

6.0 Height 107.064050 108.911650 111.988550 115.392350 118.781150 121.818900 123.631350

6.5 Height 110.018800 111.912700 115.079450 118.600800 122.125200 125.299750 127.200700

7.0 Height 112.956300 114.889600 118.136750 121.768850 125.426100 128.738850 130.730900

7.5 Height 115.827800 117.801150 121.128950 124.870950 128.659650 132.109300 134.191650

8.0 Height 118.581900 120.602700 124.020350 127.877850 131.798900 135.382400 137.551700

8.5 Height 121.178100 123.258050 126.780450 130.763450 134.819700 138.533500 140.784750

9.0 Height 123.598350 125.749300 129.392100 133.511350 137.706550 141.547650 143.876150

9.5 Height 125.853750 128.084150 131.858450 136.122000 140.459250 144.426250 146.829050

10.0 Height 127.987850 130.299600 134.208450 138.618850 143.100150 147.194100 149.671650

10.5 Height 130.075000 132.463450 136.501050 141.055450 145.681700 149.906850 152.463150

11.0 Height 132.215300 134.671800 138.827700 143.520550 148.292700 152.655600 155.297400

11.5 Height 132.21530 134.67180 138.82770 143.52055 148.29270 152.65560 155.29740

12.0 Height 134.52285 137.04195 141.30985 146.13810 151.05765 155.56365 158.29590

12.5 Height 137.10385 139.69265 144.08135 149.05025 154.11735 158.76230 161.58050

13.0 Height 140.02505 142.70795 147.24570 152.36795 157.57470 162.33325 165.21370

13.5 Height 143.27815 146.08705 150.80635 156.08705 161.40610 166.22555 169.12420

14.0 Height 146.75565 149.70525 154.60860 160.02120 165.39820 170.20860 173.07465

14.5 Height 150.25960 153.32425 158.36010 163.83840 169.20275 173.93995 176.73605

15.0 Height 153.55310 156.67090 161.74750 167.20845 172.49795 177.12450 179.83685

15.5 Height 156.43700 159.53735 164.56300 169.93990 175.12070 179.63170 182.26780

16.0 Height 158.80480 161.83570 166.75005 172.00945 177.07825 181.49250 184.07230

16.5 Height 160.64725 163.58545 168.36665 173.50575 178.47885 182.82505 185.37135

17.0 Height 162.02215 164.86845 169.52360 174.55820 179.45930 183.76485 186.29655

17.5 Height 163.01650 165.78525 170.33675 175.29040 180.14230 184.42780 186.95750

18.0 Height 163.71950 166.42970 170.90430 175.80060 180.62200 184.90095 187.43550

18.5 Height 164.20875 166.87840 171.30070 176.15990 180.96470 185.24470 187.78685

19.0 Height 164.54550 167.18945 171.57935 176.41705 181.21465 185.49985 188.04995

19.5 Height 164.77575 167.40505 171.77710 176.60450 181.40120 185.69320 188.25065

20.0 Height 164.93240 167.55475 171.91915 176.74375 181.54340 185.84255 188.40635



6

Boys’ Extended CDC Height Tables I

Table AFIII-3b. Boys’ heights in centimeters for the percentile range 0.01-25©

(suitable for evaluating cases involving percentiles in the range 0.01-5)

Percentiles

Ages (years)

0.01 0.1 1 3 5 10 25

2.0 Height 68.55707 73.03456 77.52789 79.910840 80.729770 81.991710 84.102890

2.5 Height 71.94430 76.73256 81.53775 84.176885 85.008210 86.300625 88.493865

3.0 Height 75.32309 80.28321 85.26089 88.067305 88.894195 90.188025 92.407180

3.5 Height 78.11578 83.29174 88.48600 91.332445 92.234155 93.635200 96.010620

4.0 Height 80.57716 85.99938 91.44079 94.348660 95.329380 96.843585 99.384695

4.5 Height 82.85422 88.53895 94.24380 97.242170 98.295495 99.914900 102.614150

5.0 Height 85.05264 91.00554 96.97950 100.094150 101.209950 102.921750 105.765750

5.5 Height 87.25274 93.46926 99.70776 102.959750 104.125200 105.913250 108.883550

6.0 Height 89.49633 95.96529 102.45713 105.861550 107.064050 108.911650 111.988550

6.5 Height 91.78204 98.49096 105.22361 108.789300 110.018800 111.912700 115.079450

7.0 Height 94.06996 101.01027 107.97514 111.704850 112.956300 114.889600 118.136750

7.5 Height 96.29594 103.46635 110.66212 114.553650 115.827800 117.801150 121.128950

8.0 Height 98.39112 105.79814 113.23136 117.279350 118.581900 120.602700 124.020350

8.5 Height 100.30229 107.95799 115.64077 119.838600 121.178100 123.258050 126.780450

9.0 Height 102.00781 109.92556 117.87132 122.213100 123.598350 125.749300 129.392100

9.5 Height 103.52509 111.71518 119.93425 124.416700 125.853750 128.084150 131.858450

10.0 Height 104.90996 113.37670 121.87339 126.497500 127.987850 130.299600 134.208450

10.5 Height 106.24878 114.99054 123.76324 128.535050 130.075000 132.463450 136.501050

11.0 Height 107.64575 116.65846 125.70305 130.632350 132.215300 134.671800 138.827700

11.5 Height 109.20874 118.49127 127.80664 130.632350 132.215300 134.671800 138.827700

12.0 Height 111.03654 120.59380 130.18488 132.900900 134.522850 137.041950 141.309850

12.5 Height 113.21502 123.05026 132.92031 135.437650 137.103850 139.692650 144.081350

13.0 Height 115.81374 125.90566 136.03329 138.295950 140.025050 142.707950 147.245700

13.5 Height 118.85840 129.13507 139.44810 141.460150 143.278150 146.087050 150.806350

14.0 Height 122.26805 132.60647 142.98146 144.833950 146.755650 149.705250 154.608600

14.5 Height 125.81922 136.08271 146.38251 148.247900 150.259600 153.324250 158.360100

15.0 Height 129.20640 139.29320 149.41569 151.494200 153.553100 156.670900 161.747500

15.5 Height 132.16691 142.03373 151.93545 154.383550 156.437000 159.537350 164.563000

16.0 Height 134.56328 144.21775 153.90637 156.797750 158.804800 161.835700 166.750050

16.5 Height 136.38547 145.86415 155.37637 158.706300 160.647250 163.585450 168.366650

17.0 Height 137.70411 147.05248 156.43391 160.148150 162.022150 164.868450 169.523600

17.5 Height 138.62107 147.88146 157.17462 161.199550 163.016500 165.785250 170.336750

18.0 Height 139.23769 148.44417 157.68323 161.945950 163.719500 166.429700 170.904300

18.5 Height 139.63924 148.81695 158.02712 162.465400 164.208750 166.878400 171.300700

19.0 Height 139.89205 149.05821 158.25680 162.821500 164.545500 167.189450 171.579350

19.5 Height 140.04450 149.21026 158.40845 163.062900 164.775750 167.405050 171.777100

20.0 Height 140.13093 149.30301 158.50753 163.225150 164.932400 167.554750 171.919150 ____________________________________________

©This table as well as Tables AFIII-3c; AFIII-4b, c; AFIII-5b, c; AFIII-6b, c first appeared as Additional File 3 of

Kamal and Jamil (2014)



7

Boys’ Extended CDC Height Tables II

Table AFIII-3c. Boys’ heights in centimeters for the percentile range 50-99.99

(suitable for evaluating cases involving percentiles in the range 95-99.99)

Percentiles Ages (years) 50 75 90 95 97 99 99.9 99.99

2.0 Height 86.452200 88.805250 90.926190 92.196880 93.022650 95.39175 99.88508 104.3626

2.5 Height 90.980750 93.521075 95.853805 97.271125 98.200180 100.6415 105.4467 110.2349

3.0 Height 94.959980 97.608725 100.078495 101.596950 102.599750 105.0504 110.028 114.9882

3.5 Height 98.700785 101.445200 103.962200 105.490000 106.490900 109.1366 114.3308 119.5068

4.0 Height 102.223900 105.079500 107.663450 109.216050 110.226750 113.0739 118.5153 123.9375

4.5 Height 105.603750 108.583650 111.257600 112.854400 113.890000 116.9242 122.6291 128.3138

5.0 Height 108.902350 112.015700 114.798550 116.455550 117.528400 120.7299 126.7038 132.6567

5.5 Height 112.159300 115.410250 118.315900 120.045950 121.166050 124.5098 130.7483 136.9649

6.0 Height 115.392350 118.781150 121.818900 123.631350 124.806300 128.2664 134.7582 141.2272

6.5 Height 118.600800 122.125200 125.299750 127.200700 128.435750 131.9903 138.7229 145.4318

7.0 Height 121.768850 125.426100 128.738850 130.730900 132.028350 135.665 142.6298 149.5702

7.5 Height 124.870950 128.659650 132.109300 134.191650 135.551200 139.2699 146.4657 153.6361

8.0 Height 127.877850 131.798900 135.382400 137.551700 138.970400 142.7832 150.2164 157.6234

8.5 Height 130.763450 134.819700 138.533500 140.784750 142.258350 146.1848 153.8676 161.5233

9.0 Height 133.511350 137.706550 141.547650 143.876150 145.400250 149.4609 157.4066 165.3244

9.5 Height 136.122000 140.459250 144.426250 146.829050 148.401050 152.6103 160.8294 169.0195

10.0 Height 138.618850 143.100150 147.194100 149.671650 151.291650 155.6532 164.1499 172.6167

10.5 Height 141.055450 145.681700 149.906850 152.463150 154.134500 158.6404 167.4131 176.1548

11.0 Height 143.520550 148.292700 152.655600 155.297400 157.025350 161.6611 170.7057 179.7184

11.5 Height 143.52055 148.29270 152.65560 155.29740 157.02535 164.8412 174.1566 183.4391

12.0 Height 146.13810 151.05765 155.56365 158.29590 160.08465 168.3156 177.9067 187.4639

12.5 Height 149.05025 154.11735 158.76230 161.58050 163.42620 172.1601 182.0301 191.8654

13.0 Height 152.36795 157.57470 162.33325 165.21370 167.09755 176.2971 186.4248 196.5167

13.5 Height 156.08705 161.40610 166.22555 169.12420 171.01235 180.449 190.7621 201.0387

14.0 Height 160.02120 165.39820 170.20860 173.07465 174.93105 184.2288 194.6038 204.9422

14.5 Height 163.83840 169.20275 173.93995 176.73605 178.53700 187.3309 197.6307 207.8942

15.0 Height 167.20845 172.49795 177.12450 179.83685 181.57680 189.6591 199.7816 209.8684

15.5 Height 169.93990 175.12070 179.63170 182.26780 183.95560 191.3012 201.2029 211.0697

16.0 Height 172.00945 177.07825 181.49250 184.07230 185.72415 192.4249 202.1135 211.768

16.5 Height 173.50575 178.47885 182.82505 185.37135 187.00415 193.1936 202.7058 212.1845

17.0 Height 174.55820 179.45930 183.76485 186.29655 187.92345 193.7312 203.1126 212.461

17.5 Height 175.29040 180.14230 184.42780 186.95750 188.58690 194.1209 203.4141 212.6744

18.0 Height 175.80060 180.62200 184.90095 187.43550 189.07130 194.4145 203.6535 212.86

18.5 Height 176.15990 180.96470 185.24470 187.78685 189.43020 194.6435 203.8537 213.0314

19.0 Height 176.41705 181.21465 185.49985 188.04995 189.70050 194.8271 204.0257 213.1919

19.5 Height 176.60450 181.40120 185.69320 188.25065 189.90730 194.9772 204.1754 213.3411

20.0 Height 176.74375 181.54340 185.84255 188.40635 190.06785 195.1014 204.306 213.478



8

Boys’ CDC Mass Table

Table AFIII-4a. Boys’ masses in kilograms for the percentile range 5-95

Percentiles

Ages (years)

5 10 25 50 75 90 95

2.0 Mass 10.75000 11.00000 12.00000 13.00000 14.00000 14.50000 15.50000

2.5 Mass 11.34038 11.77269 12.54737 13.49304 14.53995 15.58048 16.25286

3.0 Mass 12.04004 12.49284 13.31298 14.33022 15.47808 16.64282 17.40870

3.5 Mass 12.77432 13.25470 14.13354 15.24009 16.51213 17.82985 18.71190

4.0 Mass 13.54459 14.06194 15.01581 16.23113 17.64906 19.14285 20.15768

4.5 Mass 14.34289 14.90518 15.94806 17.28873 18.87061 20.55872 21.71872

5.0 Mass 15.16287 15.77477 16.91527 18.39252 20.15217 22.05057 23.36778

5.5 Mass 16.00271 16.66530 17.90634 19.52597 21.47388 23.59916 25.08886

6.0 Mass 16.86425 17.57606 18.91649 20.68064 22.82589 25.19766 26.88058

6.5 Mass 17.75073 18.50963 19.94723 21.85728 24.20976 26.85184 28.75472

7.0 Mass 18.66476 19.47008 21.00507 23.06508 25.63760 28.57794 30.73203

7.5 Mass 19.60750 20.46178 22.09972 24.31950 27.12974 30.39931 32.83726

8.0 Mass 20.57944 21.48914 23.24249 25.63932 28.71099 32.34252 35.09453

8.5 Mass 21.58221 22.55746 24.44522 27.04381 30.40656 34.43291 37.52334

9.0 Mass 22.62053 23.67420 25.72030 28.55097 32.23849 36.69048 40.13528

9.5 Mass 23.70365 24.85013 27.08114 30.17686 34.22359 39.12682 42.93178

10.0 Mass 24.84579 26.09977 28.54254 31.93556 36.37246 41.74354 45.90313

10.5 Mass 26.06577 27.44111 30.12035 33.83875 38.68907 44.53202 49.02907

11.0 Mass 27.38554 28.89422 31.83029 35.89479 41.17037 47.47427 52.28074

11.5 Mass 28.82787 30.47887 33.68567 38.10697 43.80579 50.54428 55.62339

12.0 Mass 30.41311 32.21138 35.69452 40.47136 46.57667 53.70983 59.01940

12.5 Mass 32.15535 34.10085 37.85616 42.97451 49.45588 56.93424 62.43105

13.0 Mass 34.05841 36.14528 40.15803 45.59148 52.40773 60.17801 65.82271

13.5 Mass 36.11220 38.32835 42.57324 48.28480 55.38832 63.40004 69.16191

14.0 Mass 38.29014 40.61740 45.05977 51.00478 58.34671 66.55846 72.41950

14.5 Mass 40.54822 42.96345 47.56175 53.69184 61.22700 69.61116 75.56846

15.0 Mass 42.82632 45.30363 50.01348 56.28106 63.97174 72.51632 78.58190

15.5 Mass 45.05220 47.56641 52.34596 58.70893 66.52689 75.23338 81.43056

16.0 Mass 47.14869 49.67931 54.49512 60.92118 68.84769 77.72501 84.08075

16.5 Mass 49.04399 51.57859 56.41047 62.88019 70.90439 79.95996 86.49404

17.0 Mass 50.68451 53.22005 58.06273 64.56997 72.68588 81.91635 88.62992

17.5 Mass 52.04709 54.58868 59.44960 65.99860 74.20086 83.58477 90.45195

18.0 Mass 53.14573 55.70376 60.59813 67.19818 75.47743 84.97192 91.93791

18.5 Mass 54.02679 56.61392 61.55983 68.22058 76.56146 86.10639 93.09545

19.0 Mass 54.74636 57.37573 62.39179 69.12322 77.51070 87.04730 93.98615

19.5 Mass 55.32342 58.00765 63.11432 69.93547 78.37844 87.89565 94.76187

20.0 Mass 55.66071 58.41105 63.63611 70.59761 79.18111 88.80644 95.71431



9

Boys’ Extended CDC Mass Tables I

Table AFIII-4b. Boys’ masses in kilograms for the percentile range 0.01-25


Percentiles

Ages (years)

0.01 0.1 1 3 5 10 25

2.0 Mass 7.28071 8.39710 9.68955 10.50000 10.75000 11.00000 12.00000

2.5 Mass 7.72515 8.89077 10.23735 11.07127 11.34038 11.77269 12.54737

3.0 Mass 8.11455 9.37126 10.82810 11.75990 12.04004 12.49284 13.31298

3.5 Mass 8.48011 9.84335 11.43176 12.47876 12.77432 13.25470 14.13354

4.0 Mass 8.83109 10.31462 12.05398 13.22765 13.54459 14.06194 15.01581

4.5 Mass 9.17273 10.78648 12.69142 13.99954 14.34289 14.90518 15.94806

5.0 Mass 9.50991 11.26017 13.34054 14.79026 15.16287 15.77477 16.91527

5.5 Mass 9.84671 11.73749 14.00003 15.60033 16.00271 16.66530 17.90634

6.0 Mass 10.18505 12.21970 14.67026 16.43323 16.86425 17.57606 18.91649

6.5 Mass 10.52375 12.70637 15.35190 17.29265 17.75073 18.50963 19.94723

7.0 Mass 10.85872 13.19499 16.04497 18.18022 18.66476 19.47008 21.00507

7.5 Mass 11.18447 13.68190 16.74892 19.09511 19.60750 20.46178 22.09972

8.0 Mass 11.49674 14.16436 17.46384 20.03531 20.57944 21.48914 23.24249

8.5 Mass 11.79546 14.64320 18.19237 21.00018 21.58221 22.55746 24.44522

9.0 Mass 12.08702 15.12501 18.94160 21.99279 22.62053 23.67420 25.72030

9.5 Mass 12.38517 15.62329 19.72422 23.02145 23.70365 24.85013 27.08114

10.0 Mass 12.71045 16.15821 20.55865 24.10017 24.84579 26.09977 28.54254

10.5 Mass 13.08855 16.75536 21.46820 25.24815 26.06577 27.44111 30.12035

11.0 Mass 13.54801 17.44351 22.47918 26.48839 27.38554 28.89422 31.83029

11.5 Mass 14.11762 18.25185 23.61820 27.84531 28.82787 30.47887 33.68567

12.0 Mass 14.82365 19.20679 24.90879 29.34155 30.41311 32.21138 35.69452

12.5 Mass 15.68677 20.32834 26.36747 30.99414 32.15535 34.10085 37.85616

13.0 Mass 16.71873 21.62622 27.99970 32.81041 34.05841 36.14528 40.15803

13.5 Mass 17.91869 23.09604 29.79606 34.78420 36.11220 38.32835 42.57324

14.0 Mass 19.26994 24.71614 31.72951 36.89295 38.29014 40.61740 45.05977

14.5 Mass 20.73761 26.44586 33.75440 39.09608 40.54822 42.96345 47.56175

15.0 Mass 22.26875 28.22651 35.80821 41.33554 42.82632 45.30363 50.01348

15.5 Mass 23.79610 29.98585 37.81658 43.53891 45.05220 47.56641 52.34596

16.0 Mass 25.24628 31.64695 39.70210 45.62612 47.14869 49.67931 54.49512

16.5 Mass 26.55240 33.14069 41.39613 47.52019 49.04399 51.57859 56.41047

17.0 Mass 27.66882 34.42025 42.85216 49.16144 50.68451 53.22005 58.06273

17.5 Mass 28.58380 35.47337 44.05719 50.52132 52.04709 54.58868 59.44960

18.0 Mass 29.32363 36.32657 45.03604 51.61034 53.14573 55.70376 60.59813

18.5 Mass 29.94074 37.03402 45.84223 52.47321 54.02679 56.61392 61.55983

19.0 Mass 30.47788 37.64330 46.52806 53.16571 54.74636 57.37573 62.39179

19.5 Mass 30.89821 38.12797 47.08440 53.70752 55.32342 58.00765 63.11432

20.0 Mass 30.97236 38.27760 47.34133 54.00392 55.66071 58.41105 63.63611



10

Boys’ Extended CDC Mass Tables II

Table AFIII-4c. Boys’ masses in kilograms for the percentile range 50-99.99



2.0 Mass 13.00000 14.00000 14.50000 15.50000 16.00000 17.11938 19.75434 22.78337

2.5 Mass 13.49304 14.53995 15.58048 16.25286 16.71114 17.93447 20.65080 23.76671

3.0 Mass 14.33022 15.47808 16.64282 17.40870 17.93684 19.23279 22.22270 25.66435

3.5 Mass 15.24009 16.51213 17.82985 18.71190 19.32767 20.72109 24.06484 27.93343

4.0 Mass 16.23113 17.64906 19.14285 20.15768 20.87348 22.39714 26.17400 30.57096

4.5 Mass 17.28873 18.87061 20.55872 21.71872 22.54351 24.22765 28.50634 33.52145

5.0 Mass 18.39252 20.15217 22.05057 23.36778 24.31082 26.17539 31.01140 36.71893

5.5 Mass 19.52597 21.47388 23.59916 25.08886 26.16319 28.21496 33.65373 40.11595

6.0 Mass 20.68064 22.82589 25.19766 26.88058 28.10516 30.33982 36.42421 43.70060

6.5 Mass 21.85728 24.20976 26.85184 28.75472 30.15486 32.56293 39.34268 47.50232

7.0 Mass 23.06508 25.63760 28.57794 30.73203 32.33779 34.91319 42.45408 51.58813

7.5 Mass 24.31950 27.12974 30.39931 32.83726 34.67984 37.42909 45.81944 56.05063

8.0 Mass 25.63932 28.71099 32.34252 35.09453 37.20137 40.15091 49.50375 60.99022

8.5 Mass 27.04381 30.40656 34.43291 37.52334 39.91346 43.11286 53.56242 66.49380

9.0 Mass 28.55097 32.23849 36.69048 40.13528 42.81627 46.33624 58.02856 72.61366

9.5 Mass 30.17686 34.22359 39.12682 42.93178 45.89870 49.82461 62.90300 79.34908

10.0 Mass 31.93556 36.37246 41.74354 45.90313 49.13929 53.56141 68.14801 86.63346

10.5 Mass 33.83875 38.68907 44.53202 49.02907 52.50804 57.50972 73.68567 94.32902

11.0 Mass 35.89479 41.17037 47.47427 52.28074 55.96908 61.61473 79.40196 102.23264

11.5 Mass 38.10697 43.80579 50.54428 55.62339 59.48391 65.80828 85.15704 110.09458

12.0 Mass 40.47136 46.57667 53.70983 59.01940 63.01463 70.01550 90.80128 117.64996

12.5 Mass 42.97451 49.45588 56.93424 62.43105 66.52676 74.16234 96.19444 124.65746

13.0 Mass 45.59148 52.40773 60.17801 65.82271 69.99132 78.18303 101.22442 130.93707

13.5 Mass 48.28480 55.38832 63.40004 69.16191 73.38556 82.02566 105.82079 136.39621

14.0 Mass 51.00478 58.34671 66.55846 72.41950 76.69237 85.65488 109.96002 141.03766

14.5 Mass 53.69184 61.22700 69.61116 75.56846 79.89796 89.05130 113.66139 144.94795

15.0 Mass 56.28106 63.97174 72.51632 78.58190 82.98798 92.20789 116.97514 148.27053

15.5 Mass 58.70893 66.52689 75.23338 81.43056 85.94217 95.12434 119.96582 151.17090

16.0 Mass 60.92118 68.84769 77.72501 84.08075 88.72895 97.80055 122.69388 153.80034

16.5 Mass 62.88019 70.90439 79.95996 86.49404 91.30181 100.23049 125.19820 156.26285

17.0 Mass 64.56997 72.68588 81.91635 88.62992 93.60081 102.39772 127.48205 158.58875

17.5 Mass 65.99860 74.20086 83.58477 90.45195 95.56146 104.27540 129.50787 160.72324

18.0 Mass 67.19818 75.47743 84.97192 91.93791 97.13182 105.83512 131.20958 162.54447

18.5 Mass 68.22058 76.56146 86.10639 93.09545 98.29880 107.07022 132.53593 163.93508

19.0 Mass 69.12322 77.51070 87.04730 93.98615 99.12701 108.03952 133.53956 164.93498

19.5 Mass 69.93547 78.37844 87.89565 94.76187 99.81592 108.93789 134.52790 166.00560

20.0 Mass 70.59761 79.18111 88.80644 95.71431 100.77840 110.19852 136.29237 168.43873



11

Girls’ CDC Height Table

Table AFIII-5a. Girls’ heights in centimeters for the percentile range 5-95

Percentiles Ages (years) 5 10 25 50 75 90 95

2.0 Height 79.25982 80.52476 82.63524 84.97556 87.31121 89.40951 90.66355

2.5 Height 83.81955 85.16965 87.43319 89.95910 92.49631 94.78938 96.16593

3.0 Height 87.53454 88.92868 91.27979 93.92359 96.60050 99.03802 100.50955

3.5 Height 90.69337 92.14235 94.59484 97.36593 100.18592 102.76610 104.32940

4.0 Height 93.78178 95.28846 97.84712 100.75100 103.72005 106.44885 108.10785

4.5 Height 96.91609 98.47854 101.14070 104.17540 107.29290 110.17130 111.92745

5.0 Height 100.11975 101.73695 104.50055 107.66365 110.92715 113.95300 115.80515

5.5 Height 103.36575 105.03845 107.90355 111.19300 114.59855 117.76675 119.71100

6.0 Height 106.60245 108.33245 111.30005 114.71405 118.25625 121.55850 123.58850

6.5 Height 109.76920 111.55880 114.63030 118.16645 121.83835 125.26430 127.37155

7.0 Height 112.80810 114.65945 117.83590 121.49135 125.28530 128.82360 130.99915

7.5 Height 115.67220 117.58700 120.86920 124.64130 128.55070 132.19125 134.42715

8.0 Height 118.33160 120.31175 123.70120 127.58925 131.61035 135.34725 137.63865

8.5 Height 120.77930 122.82770 126.32865 130.33610 134.47120 138.30550 140.65250

9.0 Height 123.03705 125.15965 128.78195 132.91990 137.18015 141.12190 143.53055

9.5 Height 125.16475 127.37305 131.13575 135.42525 139.83160 143.89965 146.38125

10.0 Height 127.27320 129.58625 133.51930 137.99015 142.56875 146.78315 149.34820

10.5 Height 129.53400 131.97620 136.11295 140.79160 145.55720 149.92100 152.56645

11.0 Height 132.16155 134.74690 139.09820 143.97795 148.90475 153.37865 156.07380

11.5 Height 135.31540 138.01795 142.52960 147.53620 152.53655 157.03190 159.71990

12.0 Height 138.91470 141.65210 146.19255 151.19010 156.14045 160.55745 163.18420

12.5 Height 142.54065 145.21335 149.64030 154.50420 159.31355 163.59770 166.14225

13.0 Height 145.66095 148.21890 152.46815 157.15405 161.80440 165.96085 168.43550

13.5 Height 147.98840 150.44340 154.53760 159.07510 163.60100 167.66475 170.09255

14.0 Height 149.56085 151.95010 155.94540 160.38870 164.83645 168.84325 171.24275

14.5 Height 150.57255 152.92870 156.87340 161.26735 165.67270 169.64715 172.02995

15.0 Height 151.21825 153.56165 157.48570 161.85770 166.24205 170.19860 172.57105

15.5 Height 151.63870 153.97975 157.89860 162.26275 166.63740 170.58345 172.94885

16.0 Height 151.92225 154.26555 158.18600 162.54885 166.91890 170.85810 173.21825

16.5 Height 152.12120 154.46835 158.39295 162.75700 167.12475 171.05895 173.41475

17.0 Height 152.26600 154.61740 158.54660 162.91255 167.27885 171.20895 173.56105

17.5 Height 152.37480 154.73000 158.66365 163.03150 167.39670 171.32320 173.67210

18.0 Height 152.45855 154.81710 158.75450 163.12400 167.48810 171.41150 173.75755

18.5 Height 152.52405 154.88545 158.82600 163.19680 167.55995 171.48055 173.82410

19.0 Height 152.57595 154.93975 158.88295 163.25470 167.61690 171.53505 173.87635

19.5 Height 152.61740 154.98315 158.92850 163.30105 167.66230 171.57830 173.91775

20.0 Height 152.65070 155.01810 158.96510 163.33830 167.69870 171.61290 173.95070



12

Table AFIII-5a: copy. Pasted here again in order to illustrate clearly calculations of

height percentile for the second checkup of M. E. (page 21)


2.0 Height 79.25982 80.52476 82.63524 84.97556 87.31121 89.40951 90.66355

2.5 Height 83.81955 85.16965 87.43319 89.95910 92.49631 94.78938 96.16593

3.0 Height 87.53454 88.92868 91.27979 93.92359 96.60050 99.03802 100.50955

3.5 Height 90.69337 92.14235 94.59484 97.36593 100.18592 102.76610 104.32940

4.0 Height 93.78178 95.28846 97.84712 100.75100 103.72005 106.44885 108.10785

4.5 Height 96.91609 98.47854 101.14070 104.17540 107.29290 110.17130 111.92745

5.0 Height 100.11975 101.73695 104.50055 107.66365 110.92715 113.95300 115.80515

5.5 Height 103.36575 105.03845 107.90355 111.19300 114.59855 117.76675 119.71100

6.0 Height 106.60245 108.33245 111.30005 114.71405 118.25625 121.55850 123.58850

6.5 Height 109.76920 111.55880 114.63030 118.16645 121.83835 125.26430 127.37155

7.0 Height 112.80810 114.65945 117.83590 121.49135 125.28530 128.82360 130.99915

7.5 Height 115.67220 117.58700 120.86920 124.64130 128.55070 132.19125 134.42715

8.0 Height 118.33160 120.31175 123.70120 127.58925 131.61035 135.34725 137.63865

8.5 Height 120.77930 122.82770 126.32865 130.33610 134.47120 138.30550 140.65250

9.0 Height 123.03705 125.15965 128.78195 132.91990 137.18015 141.12190 143.53055

9.5 Height 125.16475 127.37305 131.13575 135.42525 139.83160 143.89965 146.38125

10.0 Height 127.27320 129.58625 133.51930 137.99015 142.56875 146.78315 149.34820

10.5 Height 129.53400 131.97620 136.11295 140.79160 145.55720 149.92100 152.56645

11.0 Height 132.16155 134.74690 139.09820 143.97795 148.90475 153.37865 156.07380

11.5 Height 135.31540 138.01795 142.52960 147.53620 152.53655 157.03190 159.71990

12.0 Height 138.91470 141.65210 146.19255 151.19010 156.14045 160.55745 163.18420

12.5 Height 142.54065 145.21335 149.64030 154.50420 159.31355 163.59770 166.14225

13.0 Height 145.66095 148.21890 152.46815 157.15405 161.80440 165.96085 168.43550

13.5 Height 147.98840 150.44340 154.53760 159.07510 163.60100 167.66475 170.09255

14.0 Height 149.56085 151.95010 155.94540 160.38870 164.83645 168.84325 171.24275

14.5 Height 150.57255 152.92870 156.87340 161.26735 165.67270 169.64715 172.02995

15.0 Height 151.21825 153.56165 157.48570 161.85770 166.24205 170.19860 172.57105

15.5 Height 151.63870 153.97975 157.89860 162.26275 166.63740 170.58345 172.94885

16.0 Height 151.92225 154.26555 158.18600 162.54885 166.91890 170.85810 173.21825

16.5 Height 152.12120 154.46835 158.39295 162.75700 167.12475 171.05895 173.41475

17.0 Height 152.26600 154.61740 158.54660 162.91255 167.27885 171.20895 173.56105

17.5 Height 152.37480 154.73000 158.66365 163.03150 167.39670 171.32320 173.67210

18.0 Height 152.45855 154.81710 158.75450 163.12400 167.48810 171.41150 173.75755

18.5 Height 152.52405 154.88545 158.82600 163.19680 167.55995 171.48055 173.82410

19.0 Height 152.57595 154.93975 158.88295 163.25470 167.61690 171.53505 173.87635

19.5 Height 152.61740 154.98315 158.92850 163.30105 167.66230 171.57830 173.91775

20.0 Height 152.65070 155.01810 158.96510 163.33830 167.69870 171.61290 173.95070



13

Girls’ Extended CDC Height Tables I

Table AFIII-5b. Girls’ heights in centimeters for the percentile range 0.01-25


Percentiles Ages (years) 0.01 0.1 1 3 5 10 25

2.0 Height 67.16222 71.61497 76.08347 78.43754 79.25982 80.52476 82.63524

2.5 Height 70.70666 75.52747 80.36533 82.94459 83.81955 85.16965 87.43319

3.0 Height 73.73414 78.80039 83.88457 86.63432 87.53454 88.92868 91.27979

3.5 Height 76.17659 81.50098 86.84419 89.75984 90.69337 92.14235 94.59484

4.0 Height 78.51734 84.11120 89.72484 92.81305 93.78178 95.28846 97.84712

4.5 Height 80.90775 86.76921 92.65140 95.91353 96.91609 98.47854 101.14070

5.0 Height 83.37936 89.50407 95.65044 99.08391 100.11975 101.73695 104.50055

5.5 Height 85.91033 92.29271 98.69768 102.29595 103.36575 105.03845 107.90355

6.0 Height 88.45545 95.08809 101.74419 105.49690 106.60245 108.33245 111.30005

6.5 Height 90.96096 97.83427 104.73190 108.62590 109.76920 111.55880 114.63030

7.0 Height 93.37259 100.47574 107.60402 111.62525 112.80810 114.65945 117.83590

7.5 Height 95.63948 102.96282 110.31206 114.44800 115.67220 117.58700 120.86920

8.0 Height 97.71704 105.25592 112.82147 117.06460 118.33160 120.31175 123.70120

8.5 Height 99.56910 107.32901 115.11637 119.46735 120.77930 122.82770 126.32865

9.0 Height 101.17367 109.17576 117.20617 121.67640 123.03705 125.15965 128.78195

9.5 Height 102.53935 110.82371 119.13738 123.74790 125.16475 127.37305 131.13575

10.0 Height 103.74539 112.36494 121.01498 125.78715 127.27320 129.58625 133.51930

10.5 Height 105.00984 114.00319 123.02835 127.96140 129.53400 131.97620 136.11295

11.0 Height 106.74134 116.07818 125.44804 130.49010 132.16155 134.74690 139.09820

11.5 Height 109.42243 118.95152 128.51433 133.55915 135.31540 138.01795 142.52960

12.0 Height 113.20322 122.67966 132.18962 137.12860 138.91470 141.65210 146.19255

12.5 Height 117.54477 126.76046 136.00876 140.79520 142.54065 145.21335 149.64030

13.0 Height 121.52509 130.41778 139.34193 143.99355 145.66095 148.21890 152.46815

13.5 Height 124.54175 133.17263 141.83404 146.39210 147.98840 150.44340 154.53760

14.0 Height 126.54733 135.01332 143.50927 148.00995 149.56085 151.95010 155.94540

14.5 Height 127.79072 136.16905 144.57702 149.04425 150.57255 152.92870 156.87340

15.0 Height 128.54650 136.88398 145.25095 149.69845 151.21825 153.56165 157.48570

15.5 Height 129.01410 137.33493 145.68518 150.12010 151.63870 153.97975 157.89860

16.0 Height 129.31564 137.63095 145.97567 150.40160 151.92225 154.26555 158.18600

16.5 Height 129.52041 137.83477 146.17855 150.59740 152.12120 154.46835 158.39295

17.0 Height 129.66682 137.98177 146.32612 150.73900 152.26600 154.61740 158.54660

17.5 Height 129.77612 138.09193 146.43716 150.84485 152.37480 154.73000 158.66365

18.0 Height 129.86052 138.17700 146.52289 150.92595 152.45855 154.81710 158.75450

18.5 Height 129.92702 138.24392 146.59023 150.98925 152.52405 154.88545 158.82600

19.0 Height 129.98037 138.29741 146.64388 151.03930 152.57595 154.93975 158.88295

19.5 Height 130.02340 138.34042 146.68687 151.07915 152.61740 154.98315 158.92850

20.0 Height 130.05841 138.37528 146.72158 151.11120 152.65070 155.01810 158.96510



14

Table AFIII-5b: copy. Pasted here again in order to illustrate clearly calculations of percentile of

army-cutoff height (current age) for the second checkup of M. E. (page 32)


2.0 Height 67.16222 71.61497 76.08347 78.43754 79.25982 80.52476 82.63524

2.5 Height 70.70666 75.52747 80.36533 82.94459 83.81955 85.16965 87.43319

3.0 Height 73.73414 78.80039 83.88457 86.63432 87.53454 88.92868 91.27979

3.5 Height 76.17659 81.50098 86.84419 89.75984 90.69337 92.14235 94.59484

4.0 Height 78.51734 84.11120 89.72484 92.81305 93.78178 95.28846 97.84712

4.5 Height 80.90775 86.76921 92.65140 95.91353 96.91609 98.47854 101.14070

5.0 Height 83.37936 89.50407 95.65044 99.08391 100.11975 101.73695 104.50055

5.5 Height 85.91033 92.29271 98.69768 102.29595 103.36575 105.03845 107.90355

6.0 Height 88.45545 95.08809 101.74419 105.49690 106.60245 108.33245 111.30005

6.5 Height 90.96096 97.83427 104.73190 108.62590 109.76920 111.55880 114.63030

7.0 Height 93.37259 100.47574 107.60402 111.62525 112.80810 114.65945 117.83590

7.5 Height 95.63948 102.96282 110.31206 114.44800 115.67220 117.58700 120.86920

8.0 Height 97.71704 105.25592 112.82147 117.06460 118.33160 120.31175 123.70120

8.5 Height 99.56910 107.32901 115.11637 119.46735 120.77930 122.82770 126.32865

9.0 Height 101.17367 109.17576 117.20617 121.67640 123.03705 125.15965 128.78195

9.5 Height 102.53935 110.82371 119.13738 123.74790 125.16475 127.37305 131.13575

10.0 Height 103.74539 112.36494 121.01498 125.78715 127.27320 129.58625 133.51930

10.5 Height 105.00984 114.00319 123.02835 127.96140 129.53400 131.97620 136.11295

11.0 Height 106.74134 116.07818 125.44804 130.49010 132.16155 134.74690 139.09820

11.5 Height 109.42243 118.95152 128.51433 133.55915 135.31540 138.01795 142.52960

12.0 Height 113.20322 122.67966 132.18962 137.12860 138.91470 141.65210 146.19255

12.5 Height 117.54477 126.76046 136.00876 140.79520 142.54065 145.21335 149.64030

13.0 Height 121.52509 130.41778 139.34193 143.99355 145.66095 148.21890 152.46815

13.5 Height 124.54175 133.17263 141.83404 146.39210 147.98840 150.44340 154.53760

14.0 Height 126.54733 135.01332 143.50927 148.00995 149.56085 151.95010 155.94540

14.5 Height 127.79072 136.16905 144.57702 149.04425 150.57255 152.92870 156.87340

15.0 Height 128.54650 136.88398 145.25095 149.69845 151.21825 153.56165 157.48570

15.5 Height 129.01410 137.33493 145.68518 150.12010 151.63870 153.97975 157.89860

16.0 Height 129.31564 137.63095 145.97567 150.40160 151.92225 154.26555 158.18600

16.5 Height 129.52041 137.83477 146.17855 150.59740 152.12120 154.46835 158.39295

17.0 Height 129.66682 137.98177 146.32612 150.73900 152.26600 154.61740 158.54660

17.5 Height 129.77612 138.09193 146.43716 150.84485 152.37480 154.73000 158.66365

18.0 Height 129.86052 138.17700 146.52289 150.92595 152.45855 154.81710 158.75450

18.5 Height 129.92702 138.24392 146.59023 150.98925 152.52405 154.88545 158.82600

19.0 Height 129.98037 138.29741 146.64388 151.03930 152.57595 154.93975 158.88295

19.5 Height 130.02340 138.34042 146.68687 151.07915 152.61740 154.98315 158.92850

20.0 Height 130.05841 138.37528 146.72158 151.11120 152.65070 155.01810 158.96510



15

Girls’ Extended CDC Height Tables II

Table AFIII-5c. Girls’ heights in centimeters for the percentile range 50-99.99



2.0 Height 84.97556 87.31121 89.40951 90.66355 91.47729 93.84864 98.31714 102.76989

2.5 Height 89.95910 92.49631 94.78938 96.16593 97.06160 99.59895 104.43681 109.25762

3.0 Height 93.92359 96.60050 99.03802 100.50955 101.47025 104.09748 109.18166 114.24791

3.5 Height 97.36593 100.18592 102.76610 104.32940 105.35235 108.08694 113.43016 118.75454

4.0 Height 100.75100 103.72005 106.44885 108.10785 109.19580 112.04270 117.65635 123.25020

4.5 Height 104.17540 107.29290 110.17130 111.92745 113.08155 116.03692 121.91911 127.78057

5.0 Height 107.66365 110.92715 113.95300 115.80515 117.02485 120.08622 126.23259 132.35729

5.5 Height 111.19300 114.59855 117.76675 119.71100 120.99350 124.16155 130.56651 136.94890

6.0 Height 114.71405 118.25625 121.55850 123.58850 124.92890 128.20649 134.86259 141.49523

6.5 Height 118.16645 121.83835 125.26430 127.37155 128.76355 132.15441 139.05204 145.92535

7.0 Height 121.49135 125.28530 128.82360 130.99915 132.43590 135.94353 143.07181 150.17497

7.5 Height 124.64130 128.55070 132.19125 134.42715 135.90270 139.53005 146.87929 154.20263

8.0 Height 127.58925 131.61035 135.34725 137.63865 139.14930 142.89941 150.46496 158.00384

8.5 Height 130.33610 134.47120 138.30550 140.65250 142.19805 146.07615 153.86352 161.62343

9.0 Height 132.91990 137.18015 141.12190 143.53055 145.11510 149.13220 157.16260 165.16469

9.5 Height 135.42525 139.83160 143.89965 146.38125 148.01200 152.18956 160.50322 168.78758

10.0 Height 137.99015 142.56875 146.78315 149.34820 151.03135 155.40447 164.05451 172.67406

10.5 Height 140.79160 145.55720 149.92100 152.56645 154.29815 158.90919 167.93436 176.92770

11.0 Height 143.97795 148.90475 153.37865 156.07380 157.83115 162.69930 172.06917 181.40600

11.5 Height 147.53620 152.53655 157.03190 159.71990 161.46470 166.53264 176.09544 185.62453

12.0 Height 151.19010 156.14045 160.55745 163.18420 164.88350 169.99786 179.50782 188.98425

12.5 Height 154.50420 159.31355 163.59770 166.14225 167.78735 172.77670 182.02500 191.24069

13.0 Height 157.15405 161.80440 165.96085 168.43550 170.03760 174.82117 183.74532 192.63801

13.5 Height 159.07510 163.60100 167.66475 170.09255 171.66755 176.26873 184.93014 193.56102

14.0 Height 160.38870 164.83645 168.84325 171.24275 172.80175 177.28611 185.78205 194.24804

14.5 Height 161.26735 165.67270 169.64715 172.02995 173.57910 178.00412 186.41209 194.79042

15.0 Height 161.85770 166.24205 170.19860 172.57105 174.11365 178.51507 186.88204 195.21952

15.5 Height 162.26275 166.63740 170.58345 172.94885 174.48655 178.88285 187.23311 195.55393

16.0 Height 162.54885 166.91890 170.85810 173.21825 174.75205 179.15134 187.49606 195.81137

16.5 Height 162.75700 167.12475 171.05895 173.41475 174.94520 179.35046 187.69424 196.00860

17.0 Height 162.91255 167.27885 171.20895 173.56105 175.08865 179.50033 187.84469 196.15963

17.5 Height 163.03150 167.39670 171.32320 173.67210 175.19710 179.61482 187.96005 196.27586

18.0 Height 163.12400 167.48810 171.41150 173.75755 175.28030 179.70323 188.04913 196.36560

18.5 Height 163.19680 167.55995 171.48055 173.82410 175.34495 179.77223 188.11855 196.43545

19.0 Height 163.25470 167.61690 171.53505 173.87635 175.39555 179.82646 188.17292 196.48996

19.5 Height 163.30105 167.66230 171.57830 173.91775 175.43545 179.86937 188.21581 196.53283

20.0 Height 163.33830 167.69870 171.61290 173.95070 175.46710 179.90349 188.24979 196.56666



16

Girls’ CDC Mass Table

Table AFIII-6a. Girls’ masses in kilograms for the percentile range 5-95


2.0 Mass 10.21027 10.57373 11.23357 12.05504 12.98667 13.93766 14.56636

2.5 Mass 10.92927 11.32525 12.05142 12.96937 14.03026 15.13636 15.88117

3.0 Mass 11.59937 12.03322 12.83612 13.86523 15.07550 16.36278 17.24503

3.5 Mass 12.28941 12.76439 13.65063 14.80093 16.17571 17.66580 18.70460

4.0 Mass 13.02655 13.54403 14.51655 15.79321 17.34172 19.05012 20.26078

4.5 Mass 13.81303 14.37355 15.43360 16.83911 18.56677 20.50422 21.89857

5.0 Mass 14.63911 15.24370 16.39322 17.93048 19.84222 22.01757 23.60528

5.5 Mass 15.49221 16.14346 17.38718 19.06231 21.16595 23.58940 25.37962

6.0 Mass 16.36293 17.06557 18.41227 20.23653 22.54529 25.23117 27.23424

6.5 Mass 17.24808 18.00922 19.47219 21.46273 23.99651 26.96499 29.19363

7.0 Mass 18.15172 18.98060 20.57731 22.75684 25.54208 28.81940 31.28927

7.5 Mass 19.08445 19.99191 21.74298 24.13854 27.20679 30.82417 33.55350

8.0 Mass 20.06159 21.05933 22.98703 25.62791 29.01347 33.00478 36.01332

8.5 Mass 21.10086 22.20042 24.32678 27.24198 30.97877 35.37754 38.68497

9.0 Mass 22.21977 23.43142 25.77607 28.99138 33.10953 37.94569 41.56987

9.5 Mass 23.43315 24.76472 27.34257 30.87761 35.40016 40.69694 44.65228

10.0 Mass 24.75086 26.20662 29.02580 32.89130 37.83117 43.60256 47.89889

10.5 Mass 26.17616 27.75580 30.81581 35.01146 40.36928 46.61832 51.25997

11.0 Mass 27.70431 29.40239 32.69297 37.20600 42.96883 49.68671 54.67247

11.5 Mass 29.32220 31.12782 34.62859 39.43345 45.57454 52.74076 58.06410

12.0 Mass 31.00834 32.90552 36.58652 41.64567 48.12540 55.70873 61.35861

12.5 Mass 32.73382 34.70232 38.52567 43.79148 50.55926 58.51943 64.48148

13.0 Mass 34.46384 36.48056 40.40295 45.82073 52.81796 61.10794 67.36568

13.5 Mass 36.15988 38.20072 42.17681 47.68872 54.85247 63.42102 69.95701

14.0 Mass 37.78235 39.82438 43.81066 49.36034 56.62771 65.42211 72.21862

14.5 Mass 39.29360 41.31724 45.27615 50.81369 58.12661 67.09544 74.13430

15.0 Mass 40.66116 42.65217 46.55579 52.04247 59.35270 68.44864 75.71024

15.5 Mass 41.86076 43.81171 47.64470 53.05703 60.33077 69.51345 76.97509

16.0 Mass 42.87926 44.79020 48.55124 53.88341 61.10486 70.34372 77.97778

16.5 Mass 43.71657 45.59482 49.29646 54.56073 61.73361 71.00988 78.78270

17.0 Mass 44.38608 46.24527 49.91220 55.13695 62.28326 71.59017 79.46176

17.5 Mass 44.91287 46.77136 50.43736 55.66313 62.81874 72.15871 80.08337

18.0 Mass 45.32919 47.20798 50.91175 56.18535 63.39277 72.77175 80.69969

18.5 Mass 45.66721 47.58709 51.36665 56.73330 64.03214 73.45268 81.33385

19.0 Mass 45.94880 47.92626 51.81110 57.30428 64.72061 74.17712 81.96970

19.5 Mass 46.17154 48.21283 52.21332 57.84281 65.37978 74.86061 82.54568

20.0 Mass 46.28963 48.38346 52.47876 58.21897 65.85238 75.35165 82.95375



17

Table AFIII-6a: copy. Pasted here again in order to illustrate clearly calculations of

optimal mass for the second checkup of M. E. (page 26)


2.0 Mass 10.21027 10.57373 11.23357 12.05504 12.98667 13.93766 14.56636

2.5 Mass 10.92927 11.32525 12.05142 12.96937 14.03026 15.13636 15.88117

3.0 Mass 11.59937 12.03322 12.83612 13.86523 15.07550 16.36278 17.24503

3.5 Mass 12.28941 12.76439 13.65063 14.80093 16.17571 17.66580 18.70460

4.0 Mass 13.02655 13.54403 14.51655 15.79321 17.34172 19.05012 20.26078

4.5 Mass 13.81303 14.37355 15.43360 16.83911 18.56677 20.50422 21.89857

5.0 Mass 14.63911 15.24370 16.39322 17.93048 19.84222 22.01757 23.60528

5.5 Mass 15.49221 16.14346 17.38718 19.06231 21.16595 23.58940 25.37962

6.0 Mass 16.36293 17.06557 18.41227 20.23653 22.54529 25.23117 27.23424

6.5 Mass 17.24808 18.00922 19.47219 21.46273 23.99651 26.96499 29.19363

7.0 Mass 18.15172 18.98060 20.57731 22.75684 25.54208 28.81940 31.28927

7.5 Mass 19.08445 19.99191 21.74298 24.13854 27.20679 30.82417 33.55350

8.0 Mass 20.06159 21.05933 22.98703 25.62791 29.01347 33.00478 36.01332

8.5 Mass 21.10086 22.20042 24.32678 27.24198 30.97877 35.37754 38.68497

9.0 Mass 22.21977 23.43142 25.77607 28.99138 33.10953 37.94569 41.56987

9.5 Mass 23.43315 24.76472 27.34257 30.87761 35.40016 40.69694 44.65228

10.0 Mass 24.75086 26.20662 29.02580 32.89130 37.83117 43.60256 47.89889

10.5 Mass 26.17616 27.75580 30.81581 35.01146 40.36928 46.61832 51.25997

11.0 Mass 27.70431 29.40239 32.69297 37.20600 42.96883 49.68671 54.67247

11.5 Mass 29.32220 31.12782 34.62859 39.43345 45.57454 52.74076 58.06410

12.0 Mass 31.00834 32.90552 36.58652 41.64567 48.12540 55.70873 61.35861

12.5 Mass 32.73382 34.70232 38.52567 43.79148 50.55926 58.51943 64.48148

13.0 Mass 34.46384 36.48056 40.40295 45.82073 52.81796 61.10794 67.36568

13.5 Mass 36.15988 38.20072 42.17681 47.68872 54.85247 63.42102 69.95701

14.0 Mass 37.78235 39.82438 43.81066 49.36034 56.62771 65.42211 72.21862

14.5 Mass 39.29360 41.31724 45.27615 50.81369 58.12661 67.09544 74.13430

15.0 Mass 40.66116 42.65217 46.55579 52.04247 59.35270 68.44864 75.71024

15.5 Mass 41.86076 43.81171 47.64470 53.05703 60.33077 69.51345 76.97509

16.0 Mass 42.87926 44.79020 48.55124 53.88341 61.10486 70.34372 77.97778

16.5 Mass 43.71657 45.59482 49.29646 54.56073 61.73361 71.00988 78.78270

17.0 Mass 44.38608 46.24527 49.91220 55.13695 62.28326 71.59017 79.46176

17.5 Mass 44.91287 46.77136 50.43736 55.66313 62.81874 72.15871 80.08337

18.0 Mass 45.32919 47.20798 50.91175 56.18535 63.39277 72.77175 80.69969

18.5 Mass 45.66721 47.58709 51.36665 56.73330 64.03214 73.45268 81.33385

19.0 Mass 45.94880 47.92626 51.81110 57.30428 64.72061 74.17712 81.96970

19.5 Mass 46.17154 48.21283 52.21332 57.84281 65.37978 74.86061 82.54568

20.0 Mass 46.28963 48.38346 52.47876 58.21897 65.85238 75.35165 82.95375



18

Girls’ Extended CDC Mass Tables I

Table AFIII-6b. Girls’ masses in kilograms for the percentile range 0.01-25



2.0 Mass 6.97694 8.01541 9.21297 9.98567 10.21027 10.57373 11.23357

2.5 Mass 7.31418 8.46344 9.79835 10.68595 10.92927 11.32525 12.05142

3.0 Mass 7.56598 8.83354 10.31911 11.33412 11.59937 12.03322 12.83612

3.5 Mass 7.80799 9.20017 10.84686 12.00031 12.28941 12.76439 13.65063

4.0 Mass 8.07676 9.59794 11.41259 12.71282 13.02655 13.54403 14.51655

4.5 Mass 8.38081 10.03415 12.02130 13.47435 13.81303 14.37355 15.43360

5.0 Mass 8.71218 10.50052 12.66433 14.27482 14.63911 15.24370 16.39322

5.5 Mass 9.05567 10.98254 13.32851 15.10075 15.49221 16.14346 17.38718

6.0 Mass 9.39582 11.46610 14.00240 15.94138 16.36293 17.06557 18.41227

6.5 Mass 9.72157 11.94189 14.67999 16.79215 17.24808 18.00922 19.47219

7.0 Mass 10.02899 12.40779 15.36238 17.65584 18.15172 18.98060 20.57731

7.5 Mass 10.32215 12.86938 16.05772 18.54211 19.08445 19.99191 21.74298

8.0 Mass 10.61236 13.33907 16.77994 19.46580 20.06159 21.05933 22.98703

8.5 Mass 10.91617 13.83402 17.54651 20.44471 21.10086 22.20042 24.32678

9.0 Mass 11.25280 14.37364 18.37593 21.49713 22.21977 23.43142 25.77607

9.5 Mass 11.64148 14.97689 19.28509 22.63932 23.43315 24.76472 27.34257

10.0 Mass 12.09919 15.65988 20.28696 23.88331 24.75086 26.20662 29.02580

10.5 Mass 12.63899 16.43412 21.38868 25.23503 26.17616 27.75580 30.81581

11.0 Mass 13.26889 17.30511 22.59031 26.69289 27.70431 29.40239 32.69297

11.5 Mass 13.99121 18.27163 23.88414 28.24702 29.32220 31.12782 34.62859

12.0 Mass 14.80212 19.32534 25.25458 29.87903 31.00834 32.90552 36.58652

12.5 Mass 15.69156 20.45088 26.67870 31.56258 32.73382 34.70232 38.52567

13.0 Mass 16.64327 21.62633 28.12739 33.26459 34.46384 36.48056 40.40295

13.5 Mass 17.63517 22.82419 29.56701 34.94710 36.15988 38.20072 42.17681

14.0 Mass 18.64025 24.01284 30.96168 36.56982 37.78235 39.82438 43.81066

14.5 Mass 19.62785 25.15851 32.27589 38.09303 39.29360 41.31724 45.27615

15.0 Mass 20.56584 26.22790 33.47759 39.48095 40.66116 42.65217 46.55579

15.5 Mass 21.42331 27.19123 34.54121 40.70523 41.86076 43.81171 47.64470

16.0 Mass 22.17408 28.02562 35.45069 41.74821 42.87926 44.79020 48.55124

16.5 Mass 22.80040 28.71835 36.20188 42.60542 43.71657 45.59482 49.29646

17.0 Mass 23.29618 29.26931 36.80364 43.28650 44.38608 46.24527 49.91220

17.5 Mass 23.66859 29.69151 37.27698 43.81372 44.91287 46.77136 50.43736

18.0 Mass 23.93694 30.00896 37.65134 44.21771 45.32919 47.20798 50.91175

18.5 Mass 24.12814 30.25090 37.95774 44.53071 45.66721 47.58709 51.36665

19.0 Mass 24.26764 30.44198 38.21787 44.77714 45.94880 47.92626 51.81110

19.5 Mass 24.36517 30.58692 38.42834 44.96074 46.17154 48.21283 52.21332

20.0 Mass 24.39373 30.64892 38.53921 45.04655 46.28963 48.38346 52.47876



19

Girls’ Extended CDC Mass Tables II

Table AFIII-6c. Girls’ masses in kilograms for the percentile range 50-99.99



2.0 Mass 12.05504 12.98667 13.93766 14.56636 15.00156 16.02593 18.42033 21.16208

2.5 Mass 12.96937 14.03026 15.13636 15.88117 16.40334 17.53990 20.30640 23.49712

3.0 Mass 13.86523 15.07550 16.36278 17.24503 17.87129 19.14377 22.36325 26.10984

3.5 Mass 14.80093 16.17571 17.66580 18.70460 19.45103 20.87355 24.60961 28.99753

4.0 Mass 15.79321 17.34172 19.05012 20.26078 21.14118 22.71838 27.01367 32.10145

4.5 Mass 16.83911 18.56677 20.50422 21.89857 22.92432 24.65607 29.53893 35.36625

5.0 Mass 17.93048 19.84222 22.01757 23.60528 24.78580 26.67382 32.17039 38.77401

5.5 Mass 19.06231 21.16595 23.58940 25.37962 26.72312 28.77725 34.92434 42.35558

6.0 Mass 20.23653 22.54529 25.23117 27.23424 28.74855 30.99105 37.84628 46.18534

6.5 Mass 21.46273 23.99651 26.96499 29.19363 30.88702 33.35437 41.00204 50.36653

7.0 Mass 22.75684 25.54208 28.81940 31.28927 33.17100 35.91329 44.46510 55.01185

7.5 Mass 24.13854 27.20679 30.82417 33.55350 35.63396 38.71220 48.30300 60.22288

8.0 Mass 25.62791 29.01347 33.00478 36.01332 38.30372 41.78522 52.56390 66.06952

8.5 Mass 27.24198 30.97877 35.37754 38.68497 41.19666 45.14870 57.26476 72.57145

9.0 Mass 28.99138 33.10953 37.94569 41.56987 44.31353 48.79560 62.38254 79.68367

9.5 Mass 30.87761 35.40016 40.69694 44.65228 47.63715 52.69247 67.84984 87.28949

10.0 Mass 32.89130 37.83117 43.60256 47.89889 51.13208 56.77960 73.55645 95.20347

10.5 Mass 35.01146 40.36928 46.61832 51.25997 54.74625 60.97427 79.35679 103.18537

11.0 Mass 37.20600 42.96883 49.68671 54.67247 58.41423 65.17699 85.08286 110.96393

11.5 Mass 39.43345 45.57454 52.74076 58.06410 62.06177 69.27962 90.56028 118.26601

12.0 Mass 41.64567 48.12540 55.70873 61.35861 65.61141 73.17479 95.62565 124.84687

12.5 Mass 43.79148 50.55926 58.51943 64.48148 68.98836 76.76512 100.14211 130.51562

13.0 Mass 45.82073 52.81796 61.10794 67.36568 72.12636 79.97163 104.01179 135.15335

13.5 Mass 47.68872 54.85247 63.42102 69.95701 74.97275 82.74041 107.18394 138.72203

14.0 Mass 49.36034 56.62771 65.42211 72.21862 77.49239 85.04720 109.65817 141.26443

14.5 Mass 50.81369 58.12661 67.09544 74.13430 79.66967 86.89944 111.48346 142.89678

15.0 Mass 52.04247 59.35270 68.44864 75.71024 81.50866 88.33554 112.75249 143.79480

15.5 Mass 53.05703 60.33077 69.51345 76.97509 83.03118 89.42134 113.59253 144.17569

16.0 Mass 53.88341 61.10486 70.34372 77.97778 84.27334 90.24363 114.15265 144.27651

16.5 Mass 54.56073 61.73361 71.00988 78.78270 85.28105 90.90086 114.58811 144.32999

17.0 Mass 55.13695 62.28326 71.59017 79.46176 86.10471 91.49167 115.04293 144.53985

17.5 Mass 55.66313 62.81874 72.15871 80.08337 86.79332 92.10169 115.63145 145.05609

18.0 Mass 56.18535 63.39277 72.77175 80.69969 87.38810 92.78952 116.42024 145.95221

18.5 Mass 56.73330 64.03214 73.45268 81.33385 87.91607 93.57244 117.41132 147.20567

19.0 Mass 57.30428 64.72061 74.17712 81.96970 88.38442 94.41364 118.53001 148.68722

19.5 Mass 57.84281 65.37978 74.86061 82.54568 88.77550 95.21397 119.62349 150.16987

20.0 Mass 58.21897 65.85238 75.35165 82.95375 89.04485 95.81431 120.48086 151.37528



20

Table AFIII-6c: copy. Pasted here again in order to illustrate clearly calculations of

mass percentile for the second checkup of M. E. (page 22)


2.0 Mass 12.05504 12.98667 13.93766 14.56636 15.00156 16.02593 18.42033 21.16208

2.5 Mass 12.96937 14.03026 15.13636 15.88117 16.40334 17.53990 20.30640 23.49712

3.0 Mass 13.86523 15.07550 16.36278 17.24503 17.87129 19.14377 22.36325 26.10984

3.5 Mass 14.80093 16.17571 17.66580 18.70460 19.45103 20.87355 24.60961 28.99753

4.0 Mass 15.79321 17.34172 19.05012 20.26078 21.14118 22.71838 27.01367 32.10145

4.5 Mass 16.83911 18.56677 20.50422 21.89857 22.92432 24.65607 29.53893 35.36625

5.0 Mass 17.93048 19.84222 22.01757 23.60528 24.78580 26.67382 32.17039 38.77401

5.5 Mass 19.06231 21.16595 23.58940 25.37962 26.72312 28.77725 34.92434 42.35558

6.0 Mass 20.23653 22.54529 25.23117 27.23424 28.74855 30.99105 37.84628 46.18534

6.5 Mass 21.46273 23.99651 26.96499 29.19363 30.88702 33.35437 41.00204 50.36653

7.0 Mass 22.75684 25.54208 28.81940 31.28927 33.17100 35.91329 44.46510 55.01185

7.5 Mass 24.13854 27.20679 30.82417 33.55350 35.63396 38.71220 48.30300 60.22288

8.0 Mass 25.62791 29.01347 33.00478 36.01332 38.30372 41.78522 52.56390 66.06952

8.5 Mass 27.24198 30.97877 35.37754 38.68497 41.19666 45.14870 57.26476 72.57145

9.0 Mass 28.99138 33.10953 37.94569 41.56987 44.31353 48.79560 62.38254 79.68367

9.5 Mass 30.87761 35.40016 40.69694 44.65228 47.63715 52.69247 67.84984 87.28949

10.0 Mass 32.89130 37.83117 43.60256 47.89889 51.13208 56.77960 73.55645 95.20347

10.5 Mass 35.01146 40.36928 46.61832 51.25997 54.74625 60.97427 79.35679 103.18537

11.0 Mass 37.20600 42.96883 49.68671 54.67247 58.41423 65.17699 85.08286 110.96393

11.5 Mass 39.43345 45.57454 52.74076 58.06410 62.06177 69.27962 90.56028 118.26601

12.0 Mass 41.64567 48.12540 55.70873 61.35861 65.61141 73.17479 95.62565 124.84687

12.5 Mass 43.79148 50.55926 58.51943 64.48148 68.98836 76.76512 100.14211 130.51562

13.0 Mass 45.82073 52.81796 61.10794 67.36568 72.12636 79.97163 104.01179 135.15335

13.5 Mass 47.68872 54.85247 63.42102 69.95701 74.97275 82.74041 107.18394 138.72203

14.0 Mass 49.36034 56.62771 65.42211 72.21862 77.49239 85.04720 109.65817 141.26443

14.5 Mass 50.81369 58.12661 67.09544 74.13430 79.66967 86.89944 111.48346 142.89678

15.0 Mass 52.04247 59.35270 68.44864 75.71024 81.50866 88.33554 112.75249 143.79480

15.5 Mass 53.05703 60.33077 69.51345 76.97509 83.03118 89.42134 113.59253 144.17569

16.0 Mass 53.88341 61.10486 70.34372 77.97778 84.27334 90.24363 114.15265 144.27651

16.5 Mass 54.56073 61.73361 71.00988 78.78270 85.28105 90.90086 114.58811 144.32999

17.0 Mass 55.13695 62.28326 71.59017 79.46176 86.10471 91.49167 115.04293 144.53985

17.5 Mass 55.66313 62.81874 72.15871 80.08337 86.79332 92.10169 115.63145 145.05609

18.0 Mass 56.18535 63.39277 72.77175 80.69969 87.38810 92.78952 116.42024 145.95221

18.5 Mass 56.73330 64.03214 73.45268 81.33385 87.91607 93.57244 117.41132 147.20567

19.0 Mass 57.30428 64.72061 74.17712 81.96970 88.38442 94.41364 118.53001 148.68722

19.5 Mass 57.84281 65.37978 74.86061 82.54568 88.77550 95.21397 119.62349 150.16987

20.0 Mass 58.21897 65.85238 75.35165 82.95375 89.04485 95.81431 120.48086 151.37528



21

Evaluation of Height and Mass Percentiles

Table AFIII-7a. Height percentile using the technique of box interpolation (1st checkup)

#

h 129.50 cm

Percentile

Age (years)

P(h<) = 25 P(h) = ? P(h>) = 50

A 8.5

126.32865

130.33610

A 8.6602739726027397....

127.1144252054794

129.50

131.1643317808219

A 9.0

128.78195

132.91990

P(h) = 39.72611003575343

Hence, the percentile of height of M. E. comes out to 39.73

Table AFIII-7b. Mass percentile using the technique of box interpolation (1st checkup)

20.90 kg

Percentile

Age (years)

P(<) = 75 P() = ? P(>) = 90

A 8.5

30.97877

35.37754

A 8.6602739726027397

31.66178073972602

31.90

36.20075520547945

A 9.0

33.10953

37.94569

P() = 75.78724587042077

Hence, the percentile of mass of M. E. comes out to 75.79

____________________________________________

#Introduced and defined in Kamal et al. (2011) — step-by-step detailed calculations of results in Tables AFIII-7a-d,

along with the formulae used, are shown on pages 22-24

These values as well as values on page 22 are obtained from CDC Height Table (for girls) — reproduced on

pages 11 and 12 of this document as Tables AFIII-5a and AFIII-5a: copy

These values are obtained from CDC Mass Table (for girls) — reproduced on page 16 of this document as Table

AFIII-6a; values on page 22 are read off from Extended CDC Mass Table — reproduced on page 20 of this document

as Table AFIII-6c: copy



22

Table AFII-7c. Height percentile using the technique of box interpolation (2nd

checkup)

h 131.00 cm

Percentile

Age (years)

P(h<) = 25 P(h) = ? P(h>) = 50

A 9.0

128.78195

132.91990

A 9.1397260273972603

129.4397242465753

131.00

133.6200252054795

A 9.5

131.13575

135.42525

P(h) = 34.33112094537867

Hence, the percentile of height of M. E. comes out to 34.33

Table AFII-7d. Mass percentile using the technique of box interpolation (2nd

checkup)

21.56 kg

Percentile

Age (years)

P(<) = 50 P() = ? P(>) = 75

A 9.0

28.99138

33.10953

A 9.1397260273972603

29.51849084931507

31.79

33.74965126027397

A 9.5

30.87761

35.40016

P() = 63.42131312725474

Hence, the percentile of mass of M. E. comes out to 63.42



23

Detailed Calculations of Height Percentiles

Box interpolation, essentially, consists of two linear interpolations, one along constant-percentile

route and the other along constant-age route.

Linear interpolation along constant-percentile route, based on two-point form of equation of

straight line, may be performed using

(AFIII-1a)

)(, hPhh

hh

AA

AAconstant

which may be written as

(AFIII-1b)

)(,)( hP

AA

AAhhhh constant

Linear interpolation along constant-age route, based on two-point form of equation of straight

line, may be performed using

(AFIII-2a)

A

hh

hh

hPhP

hPhP,

)()(

)()(

12

1

12

1 constant


(AFIII-2b)

A

hh

hhhPhPhPhP ,)()()()(

12

1121 constant

-------------------------------------------------------------------------------------------------------------------------

First Checkup: Please refer to Table AFIII-5a (page 11) and Table AFIII-7a (page 21). The ages

are A 7.5 years, A 8.0 years.

To evaluate )(( hPh 25; A 8.6602739726027397 years) ,1h one uses )(( hPh

25; A 8.5 years) h cm, )(( hPh 25; A 9.0 years) h cm,

in equation (AFIII-1b), constant-percentile route, to get

5.80.9

5.8 260273978.66027397)126.32865128.78195(126.328651h 127.1144252054794 cm

To evaluate )(( hPh 50; A 8.6602739726027397 years) ,2h one uses )(( hPh 50;

A 8.5 years) h cm, )(( hPh 50; A 9.0 years) h cm, in equation (AFIII-1b), constant-percentile route, to get

5.80.9

5.8 260273978.66027397 )130.33610132.91990(130.336102h 131.1643317808219 cm

To compute percentile of height P(h), one substitutes )(hP 25, )(hP 50; h 129.50 cm,

1h 127.1144252054794 cm, 2h 131.1643317808219 cm, in equation (AFIII-2b), constant-

age route, to obtain

AhP ,

2054794127.114425 7808219131.164331

2054794127.11442550.129)2550(25)( 8.6602739726027397 years

which gives M. E.’s height percentile for her first checkup, as reported on page 21

P(h) = 39.72611003575343

-------------------------------------------------------------------------------------------------------------------------

Second Checkup: Please refer to Table AFIII-5a: copy (page 12) and Table AFIII-7c (page 22).

The ages are A 9.0 years, A 9.5 years.

128.78195

132.91990

126.32865

130.33610



24

To evaluate )(( hPh 25; A 9.1397260273972603 years) ,1h one uses )(( hPh 25; A 9.0

years) h ……………cm, )(( hPh 25; A 9.5 years) h ……………cm, in equation

(AFIII-1b), constant-percentile route, to get

0.95.9

0.9 739726039.13972602)128.78195131.13575(128.781951h 129.4397242465753 cm

To evaluate )(( hPh 50; A 9.1397260273972603 years) ,2h one uses )(( hPh 50; A

9.0 years) h ……………cm, )(( hPh 50; A 9.5 years) h …………….cm, in equa-

tion (AFIII-1b), constant-percentile route, to get

0.95.9

0.9 739726039.13972602)132.91990135.42525(132.919902h 133.6200252054795 cm

To compute percentile of height P(h), one substitutes )(hP 25, )(hP 50; h 131.00 cm,

1h 129.4397242465753 cm, 2h 133.6200252054795 cm, in equation (AFIII-2b), constant-age

route, to obtain

AhP ,

2465753129.439724 2054795133.620025

2465753129.43972400.131)2550(25)( 9.1397260273972603 years

which gives M. E.’s height percentile for her second checkup, as reported on page 22

P(h) = 34.33112094537867

-------------------------------------------------------------------------------------------------------------------------

Detailed Calculations of Mass Percentiles



(AFIII-1c)

)(,

P

AA

AAconstant


(AFIII-1d)

)(,)( P

AA

AAconstant



(AFII-2c)

A

PP

PP,

)()(

)()(

12

1

12

1

constant


(AFIII-2d)

APPPP ,)()()()(

12

1121

constant

-------------------------------------------------------------------------------------------------------------------------

First Checkup: Please refer to Table AFIII-6a (page 16) and Table AFIII-7b (page 21). The ages

are A 8.5 years, A 9.0 years.

To evaluate )(( P 75; A 8.6602739726027397 years) ,1 one uses )(( P 75; A

8.5 years) …………..kg, )(( P 75; A 9.0 years) ……………kg, in equation

(AFIII-1d), constant-percentile route, to get

128.78195

132.91990

131.13575

135.42525

30.97877 33.10953



25

5.80.9

5.8 260273978.66027397)97877.3033.10953(30.978771 31.66178073972602 kg

To evaluate )(( P 90; A 8.6602739726027397 years) ,2 one uses )(( P 90;

A 8.5 years) …………. kg, )(( P 90; A 9.0 years) ……………kg, in

equation (AFIII-1d), constant-percentile route, to get

5.80.9

5.8260273978.66027397)35.3775437.94569(35.377542 36.20075520547945 kg

To compute percentile of mass P(), one substitutes )(P 75, )(P 90; 31.90 kg,

1 31.66178073972602 kg, 2 36.20075520547945 kg, in equation (AFIII-2d), constant-age

route, to obtain

AP ,

397260231.6617807 054794536.2007552

397260231.661780790.31)7590(75)( 8.6602739726027397 years

which gives M. E.’s mass percentile for her first checkup, as reported on page 18

P() = 75.78724587042077

-------------------------------------------------------------------------------------------------------------------------

Second Checkup: Please refer to Table AFIII-6c: copy (page 20) and Table AFIII-7d (page 22).

The ages are A 9.5 years, A 9.0 years.


A 9.0 years) ………… kg, )(( P 50; A 9.5 years) …………..kg, in


0.95.9

0.9739726039.13972602)99138.2830.87761(99138.281 29.51849084931507 kg


A 9.0 years) …………..kg, )(( P 75; A 9.5 years) ……… ….kg, in


2

0.95.9

0.9739726039.13972602)33.1095335.40016(33.10953 33.74965126027397 kg

To compute percentile of mass ),(P one substitutes )(P 50, )(P 75; 1.79 kg, 1

29.51849084931507 kg, 2 33.74965126027397 kg, in equation (AFIII-2d), constant-age route, to

obtain

AP ,

493150729.5184908 602739733.7496512

493150729.518490879.31)5075(50)( 9.1397260273972603 years

which gives M. E.’s mass percentile for her second checkup, as reported on page 22

P() = 63.42131312725474

37.94569

28.99138

33.10953

30.87761

35.40016

35.37754



26

Evaluation of Height-Percentile-based-Optimal Mass, Estimated-Adult Height and Estimated-Adult Mass

Table AFIII-8a. Height-percentile-based-optimal mass and estimated-adult height (1st checkup)

Height Percentile

P(h<) = 25 39.72611003575343

P(h>) = 50

opt (kg) A[ 8.5 years]

24.32678 26.04396223904914 27.24198

opt (kg)

A[ 8.6602739726027397 years]

24.79134693150685

26.56519503217693

26.56519503217693 27.80274657534246


25.77607 27.67003035436233 28.99138

optW (lb-oz)

58 lb

9.22008073520209 oz

adult-esth (cm)

158.96510 161.5411089763343 163.33830

adult-esth (ft-in)

5 ft

3.598861801706417 in

opt)( kg

+5.33480496782307

)(STATUS %100opt

opt

+20.0819341298316%

Qualitative Status

(pertaining-to-mass)

3rd-Degree Obese

Table AFIII-8b. Estimated-adult mass and weight (1st checkup)

Mass Percentile

P(<) = 75

75.78724587042077

P(>) = 90

est-adult (kg)

65.85238 66.35093073863413

75.35165

West-adult (lb-oz)

146 lb

4.860836459012 oz

__________________________________________

Refer to Table AFIII-6a on page 16; for equivalent mass entries in Table AFIII-8c (page 27), refer to Table AFIII-

6c on page 19 The entries in blue font show alternate method of ‘constant-age route’, which could, also, be used to compute opt

as 26.56519503217693 kg, with identical result 26.56519503217693 kg as obtained from ‘constant-percentile route’.

Refer to Table AFIII-5a on page 11; for calculations of Table AFIII-8d (page 27), refer to Table AFIII-5a: copy on

page 12



27

Table AFIII-8c. Height-percentile-based-optimal mass and estimated-adult height (2nd

checkup)

Height Percentile

P(h<) = 25 34.33112094537867

P(h>) = 50


25.77607 26.97616785947542 28.99138

opt (kg)

A[ 9.1397260273972603 years]

26.21383164383562

27.44727863301913

27.44727863301913 27.80274657534246


27.34257 28.66200543147006 30.87761

optW (lb-oz)

60 lb

8.339990172915 oz

adult-esth (cm)

158.96510 160.5973743247332 163.33830

adult-esth (ft-in)

5 ft

3.227312726272913 in

opt)( kg

+4.34272136698087

)(STATUS %100opt

opt

+15.822047150994%

Qualitative Status

(pertaining-to-mass)

2nd-Degree Obese

Table AFIII-8d. Estimated-adult mass and weight (2nd

checkup)

Mass Percentile

P(<) = 50

63.42131312725474

P(>) = 75

est-adult (kg)

58.21897 62.3169854335487

65.85238

West-adult (lb-oz)

137 lb

6.54324609559828 oz

Table AFIII-8e. Computation of estimated-adult BMI

Checkup

1st

2nd

(kg/m2)

2adultest

adultest

h

25.42616724783587 24.1618150275448 adultestBMI



28

Detailed Calculations of Height-Percentile-based-Optimal Mass,

Estimated-Adult Height and Mass

Height-percentile-based-optimal mass is computed through 2 different routes, one along

‘constant-age route’ and the other along ‘constant-percentile route’, with identical results

obtained (Tables AFIII-8a and 8c; pages 26 and 27).



(AFIII-3a)

)(,)()(

)()(

optopt

optopthP

AA

AA

AA

AA

constant


(AFIII-3b)

)(,)()()()( optoptoptopt hP

AA

AAAAAA constant



(AFIII-4a)

APP

PP

hPhP

hPhP,

)()(

)()(

)()(

)()(

optopt

optopt

constant


(AFIII-4b)

A

hPhP

hPhPPPPP ,

)()(

)()()()()()( optoptoptopt constant

Estimated-adult height is computed using

(AFIII-5a)

A

hPhP

hPhPPhPhPhh ,

)()(

)()()()()(adult-est 20 years

Estimated-adult mass is computed using

(AFIII-5b)

A

PP

PPPPP ,

)()(

)()()()()(adult-est

20 years

-------------------------------------------------------------------------------------------------------------------------

First Checkup: Please refer to Table AFII-6a (page 16) and Table AFIII-8a (page 26). The ages

are A 8.5 years, A 9.0 years. The calculations based on ‘constant-age route’ are presented

first:

To evaluate P(opt 25; A 8.6602739726027397 years) ,1opt one uses P(opt 25; A

8.5 years) )(opt A …….……...kg, P(opt 25; A 9.0 years) )(opt A kg,

kg, in equation (AFIII-3b), constant-percentile route, to get

1opt 5.80.9

5.8260273978.66027397)24.3267825.77607(24.32678

24.79134693150685 kg

To evaluate P(opt 50; A 8.6602739726027397 years) ,2opt one uses P(opt 50;

A 8.5 years) )(opt A kg, P(opt 50; A 9.0 years) )(opt A

………… kg, in equation (AFIII-3b), constant-percentile route, to get

25.7760724.32678

28.99138

27.24198

5.80.9

5.8260273978.66027397)27.2419828.99138(27.241982opt

27.80274657534246 kg



29

To compute height-percentile-based-optimal mass, ,opt one substitutes )( hP 25, P(h)

9.72611003575343, )( hP 50; 1opt 24.79134693150685 kg, 2opt 27.80274657534246 kg,

in equation (AFIII-4b), constant-age route, to obtain

250 5

25357534339.7261100)315068524.7913469753424627.8027465(315068524.7913469opt

26.56519503217693 kg, A 8.6602739726027397 years

The calculations based on ‘constant-percentile route’ are presented below:

To evaluate opt (P 39.72611003575343; A 8.5 years) ,optA one uses P(opt

25; A 8.5 years) )(opt P ………… kg, P(opt 50; A 8.5 years) )(opt P

……..……kg, in equation (AFIII-4b), constant-age route, to get

2550

25357534339.7261100)24.3267827.24198(24.32678optA

26.04396223904914 kg

To evaluate opt (P 39.72611003575343; A 9.0 years) ,optB one uses P(opt 25;

A 9.0 years) )(opt P kg, P(opt 50; A 9.0 years) )(opt P

………….kg, in equation (AFIII-4b), constant-age route, to get

2550

25357534339.726110025.77607)28.99138(25.77607optB

28.66200543147006 kg

To compute height-percentile-based-optimal mass, ,opt one substitutes ,5.8 yearsA

, 260273978.66027397 yearsA ;0.9 yearsA optA 26.04396223904914.kg, optB

28.66200543147006 kg, in equation (AFIII-3b), constant-percentile route, to obtain

5.89.0

5.8 260273978.66027397)390491426.0439622 314700628.6620054( 390491426.0439622opt

26.56519503217693 kg, P 39.72611003575343

To convert height-percentile-based-optimal mass to height-percentile-based-optimal weight, one

writes optW 2.205(26.56519503217693) 58.57625504595013 lb

58 lb 16(0.57625504595013) oz 58 lb 9.22008073520209 oz

To compute estimated-adult height, one substitutes )(hP 25, P(h) 39.72611003575343,

)(hP 50; )(Ph cm, )(Ph cm, from Table AFII-5a (page 11) in

equation (AFIII-5a) to obtain

250 5

25357534339.7261100)158.96510163.33830(158.96510adult-est

h

9763343161.541108 cm 017064263.59886182.54

9763343161.541108 in

1706423.59886180 60 5 ft 17064173.59886180 in

Algebraic status (pertaining-to-mass) is evaluated using

158.96510 163.33830

27.24198

24.32678

28.99138

25.77607

298316%20.0819341% 321769326.5651950

321769326.565195090.31100%100)(

opt

opt

STATUS



30

which falls into the category of……………………...as per classification given in Table AFIII-19b

(page 59).

To compute estimated-adult mass, one substitutes )( P 75, P() 75.78724587042077,

)( P 90; )(P cm, )(P cm, from Table AFIII-6a (page 16) in

equa-tion (AFIII-5b) to obtain

750 9

75704207775.7872458)65.8523875.35165(65.85238adult-est

386341366.3509307 kg

and, therefore, estimated-adult weight comes out to

2786883146.3038023863413)66.3509307(205.2adult-est W

146 lb 16(0 6883.303802278 ) oz 146 lb 4.860836459012106 oz

-------------------------------------------------------------------------------------------------------------------------

Second Checkup: Please refer to Table AFIII-6a: copy (page 16) and Table AFIII-8c (page 27).

The ages are A 9.0 years, A 9.5 years. The calculations based on ‘constant-age route’ are

presented first.


9.0 years) )(opt A kg, P(opt 25; A 9.5 years) )(opt A ….kg,


0.95.9

0.9739726039.13972602)25.7760727.34257(25.776071opt 26.21383164383562 kg


9.0 years) )(opt A kg, P(opt 50; A 9.5 years) )(opt A ……………kg,


0.95.9

0.9739726039.13972602)28.9913830.87761(28.991382opt 29.51849084931507 kg

To compute height-percentile-based-optimal mass, ,opt one substitutes )(hP 25,

P(h) 34.33112094537867, )(hP 50; 1opt 26.21383164383562

kg, 2opt 29.51849084931507 kg, in equation (AFIII-4b), constant-age route, to obtain

250 5

25453786734.3311209) 438356226.2138316 493150729.5184908( 438356226.2138316opt

27.44727863301913 kg, A 9.1397260273972603 years


To evaluate opt (P 34.33112094537867; A 9.0 years) ,optA one uses P(opt 25; A

9.0 years) )(opt P kg, P(opt 50; A 9.0 years) )(opt P kg, in

equation (AFIII-4b), constant-age route, to get

2550

25453786734.3311209)25.7760728.99138(25.77607optA

26.97616785947542 kg

27.3425725.77607

30.8776128.99138

65.85238 75.35165

25.77607 28.99138

3rd-Degree Obese



31

To evaluate opt (P 34.33112094537867; A 9.5 years) ,optB one uses P(opt 25; A

9.5 years) )(opt P ………… kg, P(opt 50; A 9.5 years) )(opt P ……….……kg,

in equation (AFIII-4b), constant-age route, to get

2550

25453786734.3311209)27.3425730.87761(27.34257optB

28.66200543147006 kg

To compute height-percentile-based-optimal mass, ,opt one substitutes ,5.8 yearsA A

, 260273978.66027397 years ;0.9 yearsA optA 26.97616785947542 kg, optB

28.66200543147006 kg, in equation (AFIII-3b), constant-percentile route, to obtain

0.99.5

0.9 739726039.13972602)594754226.9761678 314700628.6620054(594754226.9761678opt

27.44727863301913 kg, P 34.33112094537867

To convert height-percentile-based-optimal mass to height-percentile-based-optimal weight, one

writes optW 2.205(27.44727863301913) 60.52124938580718 lb

60 lb 16(0.52124938580718) oz 60 lb 8.339990172915 oz

To compute estimated-adult height, one substitutes )(hP 25, P(h) 34.33112094537867, )( hP

50; )(Ph cm, )(Ph cm, from Table AFIII-5a (page 11) in equation

(AFIII-5a) to obtain

250 5

25453786734.3311209)158.96510163.33830(158.96510adult-est

h

3247332160.597374 cm 262729163.22731272.54

3247332160.597374 in

6272913.22731272 60 5 ft 6272913.22731272 in

Algebraic status (pertaining-to-mass) is evaluated using

50994%15.8220471% 330191327.4472786

330191327.447278679.31100%100)(

opt

opt

STATUS

which falls into the category of ‘2rd

-Degree Obese’ as per classification given in Table AFIII-19b

(page 59).

To compute estimated-adult mass, one substitutes )(P 50, P() 63.42131312725474,

)(P 75; )(P kg, )(P kg, from Table AFIII-6c (page 19) in equa-

tion (AFIII-5b) to obtain

5075

50272547463.4213131)58.2189765.85238(58.21897adult-est

33548762.3169854 kg

and therefore estimated-adult weight comes out to

158.96510 163.33830

58.21897 65.85238

30.8776127.34257

2nd-Degree Obese

8809749137.408952335487)62.3169854(205.2adult-est W

137 lb 16 809749)(0.4089528 oz 137 lb 6.54324609559828 oz



32

Mid-Parental and Army-Cutoff Heights at Current Age

Table AFIII-9a. Adult-mid-parental (Target) heights and percentiles

Father’s Height, Fh :167.80 cm • Mother’s Height, Mh :171.00 cm

Adult-MP-Height Formula Boy2

13MF hh Girl

2

13MF hh

MPadulth (cm)

171.91915 158.96510

MPadult h (cm)

175.90 162.90

MPadult h (ft-in)

5 ft 9.25196850394 in 5 ft 4.13385826772 in

MPadulth (cm)

176.74375 163.33830

MPP

25 25

MPP

45.62787588608 47.49439769505

MPP

50 50

Table AFIII-9b. Percentiles of army-cutoff heights

Army-Cutoff Height

Boy Girl

ACh (cm)

158.50753 155.01810

ACh (cm)

162.56 157.48

ACh (ft-in)

5 ft 4.00 in 5 ft 2.00 in

ACh (cm)

163.22515 158.96510

ACP

1 10

ACP

2.71801459210 19.35609323537

ACP

3 25



33

Table AFIII-10a. Mid-parental height at current age (1st checkup)

MP-Height Percentile

25

47.49439769505

50

MPCAh (cm) A[ 8.5 years]

126.32865

129.93445696172

130.33610

MPCAh (cm)

A[ 8.6602739726027397 years]

127.11505027397 130.75849621774

130.75849621774 131.16433178082


128.78195

132.50517771769

132.91990

MPCAMP )( hhcmh

–1.25849621774

)(MP inh54.2

)(Δ MP cmh

–0.49547095187

)(hSTATUS 100MP-CA

MPCA

h

hh %

–0.96245846667%

Qualitative Status

(pertaining-to-height)

Normal

TALL

Table AFIII-10b. Army-cutoff height at current age (1st checkup)

AC-Height Percentile

10

19.3560932356863

25

ACCAh (cm) A[ 8.5 years]

122.82770

125.01138097423

126.32865

ACCAh (cm)

A[ 8.6602739726027397 years]

123.57520178082 125.78314528363

125.78314528363 127.11505027397


125.15965

127.419021768508

128.78195

ACCAAC )( hhcmh

+3.71685471637

)(AC inh 54.2

)(Δ AC cmh

+1.4633286285



34

Table AFIII-10c. Mid-parental height at current age (2nd

checkup)

MP-Height Percentile

25

47.49439769505

50


128.78195

132.50517771769

132.91990

MPCAh (cm)

A[ 9.1397260273972603 years]

129.43972446575 133.20105833676

133.20105833676 133.62002520548


131.13575 134.99533875652

135.42525

MPCAMP )( hhcmh

–2.20105833676

)(MP inh54.2

)(Δ MP cmh

–0.86655840030

)(hSTATUS 100MP-CA

MPCA

h

hh %

–1.65243306941%

Qualitative Status

(pertaining-to-height)

1st-Deg Stunted

TALL

Table AFIII-10d. Army-cutoff height at current age (2nd

checkup)

AC-Height Percentile

10

19.3560932356863

25


125.15965

127.41902176851

128.78195

ACCAh (cm)

A[ 9.1397260273972603 years]

125.78189178082 128.06203341052

128.06203341052 129.43972424658


127.37305

129.719994801195

131.13575

ACCAAC )( hhcmh

+2.93796658948

)(AC inh54.2

)(Δ AC cmh

+1.56679759638



35

Detailed Calculations of Mid-Parental and Army-Cutoff Heights (Adult and Current Age)

For boys, adult-mid-parental (target) height is computed using the expression (heights of

biological parents in cm):

(AFIII-6a) 90.1752

1300.17180.167

2

13MFMPadult

hhh cm

039370169.25196852.54

175.90 in

53937019.2519685060 ft 3937019.25196850 in

whereas for girls, the formula takes the form

(AFIII-6b) 90.1622

1300.17180.167

2

13MFMPadult

hhh cm

677165464.13385822.54

162.90 in

57716544.1338582660 ft 7716544.13385826 in

To compute percentile of mid-parental height, linear interpolation, based on two-point form of

equation of straight line, may be performed using

(AFIII-7a)

MPadultMPadult

MPadultMPadult

MPMP

MPMP

hh

hh

PP

PP


(AFIII-7b)

MPadultMPadult

MPadultMPadultMPMPMPMP

hh

hhPPPP

Percentile of cutoff height for induction into the Armed Forces of Pakistan may be calculated by

employing linear interpolation

(AFIII-8a)

ACAC

ACAC

ACAC

ACAC

hh

hh

PP

PP


(AFIII-8b)

ACAC

ACACACACACAC

hh

hhPPPP

To compute boy’s adult-mid-parental (target) height, one notes that equation (AFIII-6a) gives

90.175MPadult h cm. To compute the percentile, one should refer to Table AFIII-3a (page 5) and

Table AFIII-9a (page32), one gets MPadulth cm; MPadulth cm;

;25MP P ;50MP P equation (AFIII-7b) gives

860845.6278758171.91915 176.74375

171.9191590.175)2550(25MP

P

To compute girl’s adult-mid-parental (target) height, one notes that equation (AFII-6b) gives

90.162MPadult h cm. To compute the percentile, one should refer to Table AFII-5a (page 11) and

Table AFIII-9a (page32), one gets MPadulth cm; MPadulth cm;

;25MP P ;50MP P equation (AFIII-7b) gives

950547.4943976158.96510 163.33830

158.9651090.162)2550(25MP

P

171.91915

158.96510 163.33830

176.74375



36

To compute boy’s army-cutoff height for the Pakistani population in cm, one notes that the

height is 5 ft 4.00 in, which may be written as

56.162)54.2(64644)12(5 4.00 5 ininft cm

To compute the percentile, one should refer to Table AFIII-3b (page 6) and Table AFIII-9b

(page32), one gets ACh ………………cm; ACh ………..……..cm; ;1AC P ;3AC P equ-

ation (AFIII-8b) gives

2102.71801459158.50753 163.22515

158.5075356.162)13(1AC

P

To compute girl’s army-cutoff height for the Pakistani population in cm, one notes that the

height is 5 ft 2.00 in, which may be written as

48.157)54.2(62622)12(5 2.00 5 ininft cm

To compute the percentile, one should refer to Table AFIII-5b (page 13) and Table AFIII-9b

(page32), one gets ACh cm; ACh cm; ;10AC P ;25AC P

equation (AFIII-8b) gives

353719.3560932155.01810 158.96510

155.0181048.157)1025(10AC

P

-------------------------------------------------------------------------------------------------------------------------

Current-age-mid-parental and current-age-army-cutoff heights are computed through 2 different

routes, one along ‘constant-age route’ and the other along ‘constant-percentile route’, with

identical results obtained (Tables AFII-10a-d; pages 34 and 35).



(AFIII-9a)

)(,)()(

)()(

)()(

)()(

AC-CAAC-CA

AC-CAAC-CA

MP-CAMP-CA

MP-CAMP-CA hPAhAh

AhAh

AhAh

AhAh

AA

AAconstant

which may be written as (the constant may be different for the second fraction and the third fraction)

(AFIII-9b)

)(,)()()()( MP-CAMP-CAMP-CAMP-CA hP

AA

AAAhAhAhAh constant

(AFIII-9c)

)(,)()()()( AC-CAAC-CAAC-CAAC-CA hP

AA

AAAhAhAhAh constant



(AFIII-10a)

APhPh

PhPh

PP

PP,

)()(

)()(

MPMP-CAMPMP-CA

MPMP-CAMPMP-CA

MPMP

MPMP constant

(AFIII-10b)

APhPh

PhPh

PP

PP,

)()(

)()(

ACAC-CAACAC-CA

ACAC-CAACAC-CA

ACAC

ACAC constant


(AFIII-10c) ,)()()()(MPMP

MPMPMPMP-CAMPMP-CAMPMP-CAMPMP-CA

PP

PPPhPhPhPh

A constant

158.50753 163.22515

155.01810 158.96510



37

(AFIII-10d) ,)()()()(ACAC

ACACACCA-CAACAC-CAACAC-CAACAC-CA

PP

PPPhPhPhPh

A constant

-------------------------------------------------------------------------------------------------------------------------

First Checkup: To evaluate mid-parental height at current age, ,MP-CAh please refer to Table

AFIII-10a (page 33) and Table AFIII-5a (page 11). The ages are A 8.5 years, A 9.0 years. The

calculations based on ‘constant-age route’ are presented first:

To evaluate MPMP-CA (Ph 25; A 8.6602739726027397 years) ,1MP-CAh one uses

MPMP-CA (Ph 25; A 8.5 years) )(MPCA Ah cm, MPMP-CA (Ph 25; A

9.0 years) )(MPCA Ah cm, in equation (AFIII-9b), constant-percentile route, to

get

5.80.9

5.8260273978.66027397)26.328651128.78195(26.3286511MP-CAh 127.11505027397 cm


MPMP-CA (Ph 50; A 8.5 years) )(MPCA Ah …………….cm, MPMP-CA (Ph 50; A


get

5.80.9

5.8260273978.66027397).33610130.91990132(.336101302MP-CAh 131.16433178082 cm

To compute mid-parental height at current age, ,MP-CAh one substitutes MPP 25, MPP

47.49439769505, MPP 50; 1MP-CAh 127.11505027397 cm, 2MP-CAh 131.16433178082 cm, in

equation (AFIII-10c), ‘constant-age route’, to obtain

250 5

25950547.4943976)27397127.115050 78082131.164331( 27397127.115050MP-CA

h

130.75849621774 cm, A 8.6602739726027397 years


To evaluate MPMP-CA (Ph 47.49439769505; A 8.5 years) ,MPA-CAh one uses

MPMP-CA (Ph 25; A 8.5 years) )( MPMP-CA Ph cm, MPMP-CA (Ph 50;

A 8.5 years) )( MPMP-CA Ph cm, in equation (AFIII-10c), constant-age route,

to get

2550

25950547.4943976)26.32865133610.130(26.328651MPA-CA

h 129.93445696172 cm

To evaluate MPMP-CA (Ph 47.49439769505; A 9.0 years) ,MPB-CAh one uses

MPMP-CA (Ph 25; A 9.0 years) )( MPMP-CA Ph cm, MPMP-CA (Ph 50;

A 9.0 years) )( MPMP-CA Ph cm, in equation (AFIII-10c), constant-age

route, to get

128.78195

132.91990

130.33610

126.32865

130.33610

128.78195

132.91990

126.32865



38

2550

25950547.4943976)28.7819512.9199013(28.781951MPB-CA

h 132.50517771769 cm

To compute mid-parental height at current age, ,MP-CAh one substitutes A 8.5 years,

, 260273978.66027397 yearsA ;0.9 yearsA MPA-CAh 129.93445696172 cm, MPB-CAh

132.50517771769 cm, in equation (AFIII-9b), ‘constant-percentile route’, to obtain

5.89.0

5.8 260273978.66027397)617229.93445691 7692.5051777113( 617229.93445691MP-CA

h

130.75849621774 cm, MPP 47.49439769505

Algebraic status (pertaining-to-height) is evaluated using

6673%0.96245846% 21774130.758496

21774130.75849650.129100%100)(

MP-CA

MP-CA

h

hhhSTATUS


-Degree Obese’ as per classification given in Table AFIII-19a

(page 59).

To evaluate army-cutoff height at current age, ,AC-CAh please refer to Table AFIII-10b (page

33) and Table AFIII-5b (page 13). The ages are A 8.5 years, A 9.0 years. The calculations

based on ‘constant-age route’ are presented first:

To evaluate ACAC-CA (Ph 10; A 8.6602739726027397 years) ,1AC-CAh one uses

ACAC-CA (Ph 10; A 8.5 years) )(ACCA Ah cm, ACAC-CA (Ph 10;

A 9.0 years) )(ACCA Ah cm, in equation (AFIII-9c), constant-percentile

route, to get

5.80.9

5.8260273978.66027397)22.827701125.15965(22.8277011AC-CAh 123.57520178082 cm


ACAC-CA (Ph 25; A 8.5 years) )(ACCA Ah cm, ACAC-CA (Ph 25; A

9.0 years) )(ACCA Ah cm, in equation (AFIII-9c), constant-percentile route, to

get

5.80.9

5.8260273978.66027397).32865126.78195128(.328651262AC-CAh 127.11505027397 cm

To compute army-cutoff height at current age, ,AC-CAh one substitutes ACP 10, ACP

19.3560932356863, ACP 25, 1AC-CAh 123.57520178082 cm, 2AC-CAh 127.11505027397 cm,

in equation (AFIII-10d), ‘constant-age route’, to obtain

10 25

1035686319.3560932)78082123.575201 27397127.115050( 78082123.575201AC-CA

h

125.78314528363 cm, A 8.6602739726027397 years


To evaluate ACAC-CA (Ph 19.3560932356863; A 8.5 years) ,ACA-CAh one uses

ACAC-CA (Ph 10; A 8.5 years) )( ACAC-CA Ph ………...…..cm, ACAC-CA (Ph 25;

126.32865

122.82770

128.78195

Normal

125.15965

122.82770



39

A 8.5 years) )( ACCA-CA Ph cm, in equation (AFIII-7c), constant-age route,

to get

1025

1035686319.3560932)122.8277032865.126(122.82770ACA-CA

h 125.01138097423 cm

To evaluate ACAC-CA (Ph 19.3560932356863; A 9.0 years) ,ACB-CAh one uses

ACAC-CA (Ph 10; A 9.0 years) )( ACAC-CA Ph cm, ACAC-CA (Ph 25; A

9.0 years) )( ACCA-CA Ph cm, in equation (AFIII-7c), constant-age route, to get

1025

1035686319.3560932)25.15965128.781951(25.159651ACB-CA

h 127.419021768508 cm

To compute army-cutoff height at current age, ,AC-CAh one substitutes A 8.5 years,

, 260273978.66027397 yearsA ,0.9 yearsA ACA-CAh 125.01138097423 cm, ACB-CAh


5.89.0

5.8 260273978.66027397) 97423125.011380 768508127.419021( 97423125.011380MP-CA

h

125.78314528363 cm, ACP 19.3560932356863

-------------------------------------------------------------------------------------------------------------------------

Second Checkup: To evaluate mid-parental height at current age, ,MP-CAh please refer to Table

AFIII-10c (page 34) and Table AFII-5a: copy (page 12). The ages are A 9.0 years, A 9.5

years. The calculations based on ‘constant-age route’ are presented first:

To evaluate MPMP-CA (Ph 25; A 9.1397260273972603 years) ,1MP-CAh one

uses MPMP-CA (Ph 25; A 9.0 years) )(MPCA Ah cm, MPMP-CA (Ph 25;

A 9.5 years) )(MPCA Ah …………....cm, in equation (AFIII-9b), constant-percentile

route, to get

0.95.9

0.9 739726039.13972602)28.781951131.78195(28.7819511MP-CAh 129.43972446575 cm


MPMP-CA (Ph 50; A 9.0 years) )(MPCA Ah cm, MPMP-CA (Ph 50; A


get

0.95.9

0.9 739726039.13972602)132.91990.42525135(132.919902MP-CAh 133.62002520548 cm

To compute mid-parental height at current age, ,MP-CAh one substitutes MPP 25, MPP

47.49439769505, MPP 50; 1MP-CAh 129.43972446575 cm, 2MP-CAh 133.62002520548 cm,

in equation (AFIII-10c), ‘constant-age route’, to obtain

250 5

25950547.4943976)46575129.439724 20548133.620025( 46575129.439724MP-CA

h

133.20105833676 cm, A 9.1397260273972603 years

128.78195

135.42525

132.91990

131.13575

125.15965

128.78195

126.32865



40


To evaluate MPMP-CA (Ph 47.49439769505; A 9.0 years) ,MPA-CAh one uses MP-CAh

MP(P 25; A 9.0 years) )(MP-CA Ph cm, MPMP-CA (Ph 50; A 9.0 years)

)(MP-CA Ph cm, in equation (AFIII-10c), constant-age route, to get

2550

25950547.4943976)128.7819591990.132(128.78195MPA-CA

h 132.50517771769 cm

To evaluate MP-CAh (P. .47.49439769505; A 9.5.years) ,MPB-CAh one uses MPMP-CA (Ph

25; A 9.5 years) )(MP-CA Ph ……….…… cm, MP-CAh MP(P 50; A 9.5 years)

)(MP-CA Ph cm, in equation (AFIII-10c), constant-age route, to get

2550

25950547.4943976)131.13575.42525135(131.13575MPB-CA

h 134.99533875652 cm

To compute mid-parental height at current age, ,MP-CAh one substitutes A 9.0 years,

, 739726039.13972602 yearsA ,5.9 yearsA MPA-CAh 132.50517771769 cm, MPB-CAh


0.99.5

0.9 739726039.13972602)71769132.505177 75652134.995338( 71769132.505177MP-CA

h

133.20105833676 cm, P 47.49439769505

Algebraic status (pertaining-to-height) is evaluated using

941%1.65243306%33676133.201058

33676133.20105800.131100%100)(

MP-CA

MP-CA

h

hhhSTATUS


-Degree Obese’ as per classification given in Table AFIII-19a

(page 59).

To evaluate army-cutoff height at current age, ,AC-CAh please refer to Table AFIII-10b (page

33) and Table AFII-5b (page 13). The ages are A 8.5 years, A 9.0 years. The calculations

based on ‘constant-age route’ are presented first:


ACAC-CA (Ph 10; A 9.0 years) )(ACCA Ah cm, ACAC-CA (Ph 10;

A 9.5 years) )(ACCA Ah cm, in equation (AFIII-9c), constant-percentile

route, to get

0.95.9

0.9 739726039.13972602 )125.15965127.37305(125.159651AC-CAh 125.78189178082 cm


ACAC-CA (Ph 25; A 9.0 years) )(ACCA Ah cm, ACAC-CA (Ph 25; A

9.5 years) )(ACCA Ah cm, in equation (AFIII-9c), constant-percentile route, to

get

0.95.9

0.9 739726039.13972602 )128.78195.13575131(128.781952AC-CAh 129.43972424658 cm

128.78195

132.91990

131.13575

135.42525

1st-Degree Stunted

128.78195

125.15965

127.37305

131.13575



41

To compute army-cutoff height at current age, ,AC-CAh one substitutes ACP 10, ACP

19.3560932356863, ACP 25, 1AC-CAh 125.78189178082 cm, 2AC-CAh 129.43972424658 cm,

in equation (AFIII-7d), ‘constant-age route’, to obtain

10 25

1035686319.3560932)78082125.781891 24658129.439724(78082125.781891AC-CA

h

128.06203341052 cm, A 8.6602739726027397 years


To evaluate ACAC-CA (Ph 19.3560932356863; A 8.5 years) ,ACA-CAh one uses

ACAC-CA (Ph 10; A 8.5 years) )( ACAC-CA Ph ………...…..cm, ACAC-CA (Ph 25;

A 8.5 years) )( ACCA-CA Ph cm, in equation (AFIII-10c), constant-age route,

to get

1025

1035686319.3560932)125.1596578195.128(125.15965ACA-CA

h 127.41902176851 cm

To evaluate ACAC-CA (Ph 19.3560932356863; A 9.0 years) ,ACB-CAh one uses

ACAC-CA (Ph 10; A 9.0 years) )( ACAC-CA Ph cm, ACAC-CA (Ph 25; A

9.0 years) )( ACCA-CA Ph cm, in equation (AFIII-10c), constant-age route, to get

1025

1035686319.3560932)127.37305.13575131(127.37305MPB-CA

h 129.719994801195 cm

To compute army-cutoff height at current age, ,AC-CAh one substitutes A 9.0 years,

, 739726039.13972602 yearsA ,5.9 yearsA ACA-CAh 127.41902176851 cm, ACB-CAh


0.99.5

0.9 739726039.1397260276851)127.419021 801195129.719994( 76851127.419021MP-CA

h

128.06203341052 cm, ACP 19.3560932356863

128.78195

125.15965

127.37305

131.13575



42

Build, Nutritional Status and Reference Percentile

Table AFIII-11. Determination of build

Checkup

1st 2

nd

)(hP

39.72611003575343 34.33112094537867

)(P

75.78724587042077 63.42131312725474

Sum )()( PhP

115.5133559061742 97.75243407263341

Range of Sum

150)()(50 PhP 150)()(50 PhP

Build

Medium Medium

Table AFIII-12. Determination of nutritional status

___________________________________________

Taken from Tables AFIII-7a, c on pages 21 and 22

),( 0AhP

Taken from Tables AFIII-7b, d on page 21 and 22

),( 0AP

As per classification given in Table AFIII-18c (page 58)



As per classification given in Figure AFIII-1 (page 60)

Checkup

1st 2

nd

)(hSTATUS

–0.962458466673% –1.65243306941%

Sign of )(hSTATUS

0)( hSTATUS 0)( hSTATUS

)(STATUS

+20.0819341298316% +15.822047150994%

Sign of )(STATUS

0)( STATUS 0)( STATUS

Nutritional Status

EC II EC II



43

Table AFIII-13. Computation of percentile of reference height

Checkup

1st 2

nd

)(yearsA

8.6602739726027397 9.1397260273972603

)(hP

39.72611003575343 34.33112094537867

MPP

47.49439769505 47.49439769505

ACP

19.35609323537 19.35609323537

),),(( ACMPref PPhPmaxP

47.49439769505 47.49439769505

___________________________________________

0A

Taken from Table AFIII-9a on page 32

Taken from Table AFIII-9b on page 32



44

Evaluation of BMI-based-Optimal Mass

Table AFIII-14a. Computation of estimated-adult-BMI-based-optimal mass (1st checkup)

Mass Percentile

< 2adultest24 h

>

adultestBMI (kg)

58.21897 62.62905662076135

65.85238

Table AFIII-14b. Computation of BMI-based-optimal mass (1st checkup)

)( BMIP

Age (years)

50 64.45670945475662 75

A 8.5

27.24198 29.4028474929376

30.97877

A 8.66027397260268

27.80274657534226 30.03430400296114

30.03430400296114

31.66178073972577

A 9.0

28.99138 31.37277592164424

33.10953

Table AFIII-14c. Computation of estimated-adult-BMI-based-optimal mass (2nd

checkup)

Mass Percentile

< 2adultest24 h

>

adultestBMI (kg)

58.21897 61.89963993599618

65.85238

Table AFIII-14d. Computation of BMI-based-optimal mass (2nd

checkup)

)BMI(P

Age (years)

50 62.05447478910533 75

A 9.0

28.99138 30.9770654141016

33.10953

A 9.13972602739727

29.51849084931511 31.55866750941769

31.55866750941769

33.74965126027402

A 9.5

30.87761 33.05828859829873

35.40016

___________________________________________

Estimated-adult height for this table taken from Table AFIII-8a (page 26) and converted to m (meters) for

substitution

in formula; for Table AFIII-14c, value is taken from Table AFIII-8c (page 27) and converted to m.



45

Detailed Calculations of BMI-based-Optimal Mass

Percentile of BMI-based-optimal mass is computed using linear interpolation from estimated-

adult-BMI-based-optimal mass

(AFIII-15a) ,24 2adultestadultestBMI h adultesth in m

24 kg/m2 is taken as reference BMI.

(AFIII-15b)

APP

PP,

)()(

)()(

adult-est-BMIadult-est-BMI


BMIBMI

BMIBMI

20 years

Equation (AFII-15b) is expressed as

(AFIII-15c)


adult-est-BMIadult-est-BMIBMIBMIBMIBMI )()()()(

PPPP

BMI-based-optimal mass is computed through 2 different routes, one along ‘constant-age

route’ and the other along ‘constant-percentile route’, with identical results obtained (Table

AFIII-14b; page 44).



(AFIII-16a)

)(,)()(

)()(BMI

BMIBMI

BMIBMI

P

AA

AA

AA

AAconstant


(AFIII-16b)

)(,)()()()( BMIBMIBMIBMIBMI P

AA

AAAAAA constant



(AFIII-17a)

APP

PP

PP

PP,

)()(

)()(

BMIBMI

BMIBMI

constant


(AFIII-17b)

A

PP

PPPPPP ,)()()()( BMIBMIBMIBMI constant

First Checkup: From Table III-8a (page 26) adultesth 161.5411089763343 cm

1.615411089763343 m

Hence

207613562.6290566)97633431.61541108(2424 22adultestadultestBMI h kg/m

2

Percentile of BMI-based-optimal mass is computed by the technique of linear interpolation using

equation (AFIII-15c). From Table AFIII-14a (page 44) and Table AFIII-6c (page 19)

adultestBMI …………..kg, adultestBMI …………..kg, ,50)( BMI P )( BMIP 75,

which gives

BMI 547566264.4567094

21897.5885238.65

21897.58207613562.6290566)5075(50)(

P

58.21897 65.85238



46

To evaluate BMI-based-optimal mass, ,BMI please refer to Table AFIII-14b (page 44) and

Table AFIII-6c (page 19). The ages are A 8.5 years, A 9.0 years. The calculations based on

‘constant-age route’ are presented first:

To evaluate )(( BMIBMI P 50; A 8.66027397260268 years) ,1BMI one uses

)(( BMIBMI P 50; A 8.5 years) )(BMI A ……..……kg, )(( BMIBMI P 50; A

9.0 years) )(BMI A ………… kg, in equation (AFIII-16b), constant-percentile route, to get

5.80.9

5.8 2602688.66027397)27.24198.9913828(27.241981BMI

27.80274657534226 kg


)(( BMIBMI P 75; A 8.5 years) )(BMI A …………..kg, )(( BMIBMI P 75; A

9.0 years) )(BMI A …………..kg, in equation (AFIII-16b), constant-percentile route, to get

5.80.9

5.8 2602688.66027397)30.8776133.10953(30.877612BMI

31.66178073972577 kg

To compute BMI-based-optimal mass, ,BMI one substitutes )( BMIP 50, )( BMIP

,547566264.4567094 )( BMIP 75, 1BMI 27.80274657534226 kg, 2BMI

31.66178073972577 kg, in equation (AFIII-17b), ‘constant-age route’, to obtain

50 75

50547566264.4567094)753422627.8027465 397257731.6617807(753422627.8027465BMI

30.03430400296114 kg, A 8.66027397260268 years


To evaluate )(( BMIBMI P 64.45670945475662; A 8.5.years) ,BMIA one uses

)(( BMIBMI P 50; A 8.5.years) ))(( BMIBMI P ……..……kg, )(( BMIBMI P 75;

A 8.5 .years) ))(( BMIBMI P …… …….kg, in equation (AFIII-17b), constant-age route,

to get

5075

50547566264.4567094)27.2419830.97877(27.24198BMIA

29.4028474929376 kg

To evaluate )(( BMIBMI P 64.45670945475662; A 9.0.years) ,BMIB one uses

)(( BMIBMI P 50; A 9.0.years) ))(( BMIBMI P ………….kg, )(( BMIBMI P 75;

A 9.0 years) ))(( BMIBMI P …… …….kg, in equation (AFIII-17b), constant-age route,

to get

5075

50547566264.4567094)28.9913833.10953(28.99138BMIB

31.37277592164424 kg

28.99138

33.10953

30.87761

27.24198

27.24198

30.87761

28.99138

33.10953



47

To compute BMI-based-optimal mass, ,BMI one substitutes A 8.5 years, A

, 2602688.66027397 years ,0.9 yearsA BMIA 29.4028474929376 kg, BMIB

31.37277592164424 kg, in equation (AFIII-16b), ‘constant-percentile route’, to obtain

5.89.0

5.8 2602688.66027397) 92937629.4028474 216442431.3727759( 92937629.4028474BMI

30.03430400296114 kg, )( BMIP 64.45670945475662

Second Checkup: From Table III-8c (page 27) adultesth 160.5973743247332 cm

1.605973743247332 m

Hence

359961861.8996399)32473321.60597374(2424 22adultestadultestBMI h kg/m

2

Percentile of BMI-based-optimal mass is computed by the technique of linear interpolation using

equation (AFII-15c). From Table AFIII-14b (page 44) and Table III-6c: copy (page 20)

adultestBMI …………..kg, adultestBMI …………..kg, ,50)( BMI P )( BMIP 75,

which gives

BMI 891053362.0544747

21897.5885238.65

21897.58359961861.8996399)5075(50)(

P

To evaluate BMI-based-optimal mass, ,BMI please refer to Table AFIII-14d (page 44) and

Table AFIII-6c: copy (page 20). The ages are A 9.0 years, A 9.5 years. The calculations based

on ‘constant-age route’ are presented first:


)(( BMIBMI P 50; A 9.0 years) )(BMI A ……..……kg, )(( BMIBMI P 50; A

9.5 years) )(BMI A ………… kg, in equation (AFIII-16b), constant-percentile route, to get

0.95.9

0.9 7397279.13972602).9913828.8776130(.99138281BMI

29.51849084931511 kg


)(( BMIBMI P 75; A 9.0 years) )(BMI A …………..kg, )(( BMIBMI P 75; A

9.5 years) )(BMI A …………..kg, in equation (AFIII-16b), constant-percentile route, to get

0.95.9

0.9 7397279.13972602)33.1095335.40016(33.109532BMI

33.74965126027402 kg

To compute BMI-based-optimal mass, ,BMI one substitutes )( BMIP 50, )( BMIP

,547566264.4567094 )( BMIP 75, 1BMI 29.51849084931511 kg, 2BMI

33.74965126027402 kg, in equation (AFIII-17b), ‘constant-age route’, to obtain

50 75

50891053362.0544747)493151129.5184908 602740233.7496512(493151129.5184908

BMI

31.55866750941769 kg, A 9.13972602739727 years

58.21897 65.85238

28.99138

30.87761

33.10953

35.40016



48


To evaluate )(( BMIBMI P 62.05447478910533; A 9.0.years) ,BMIA one uses

)(( BMIBMI P 50; A 9.0.years) ))(( BMIBMI P ……..……kg, )(( BMIBMI P 75;


to get

5075

50891053362.0544747)28.9913833.10953(28.99138BMIA

30.9770654141016 kg

To evaluate )(( BMIBMI P 62.05447478910533; A 9.5.years) ,BMIB one uses

)(( BMIBMI P 50; A 9.5.years) ))(( BMIBMI P ………….kg, )(( BMIBMI P 75;


to get

5075

50891053362.0544747)30.8776135.40016(30.87761BMIB

33.05828859829873 kg

To compute BMI-based-optimal mass, ,BMI one substitutes A 9.0 years, A

, 7397279.13972602 years ,5.9 yearsA BMIA 30.9770654141016 kg, BMIB


0.99.5

0.9 7397279.13972602) 14101630.9770654 982987333.0582885( 14101630.9770654BMI

31.55866750941769 kg, )( BMIP 62.05447478910533

28.99138

33.10953

30.87761

35.40016



49

Control-Action Trajectories for Height and Mass Percentiles

Equations for percentile of height

(AFIII-18a) ;),( refPAhP if ref0),( PAhP

(AFIII-18b) ),(),( 0refref AhPPPAhP ;10

102

0

A

Aotherwise

where refP is the value of reference percentile at the most-recent checkup, which is used for

computing 6-month recommendations. In the case of M. E., ),( 0AhP ……………………………… ,

refP ……………………and 739726039.139726020 A years. Hence

ref0 ),( PAhP

and one has to apply equation (AFIII-18b)

2

10726031397202739.9

10)78673311209453.3454943976950.47(54943976950.47),(

AAhP


Equations for percentile of mass

(AFIII-19a) ;),( refPAP if ref0),( PAP

(AFIII-19b) ),(),( 0refref APPPAP ;10

102

0

A

Aotherwise

In the case of M. E., ),( 0AP ………………………… ... …, refP ……………… …… and 0A

9.139720273972603 years. Hence

ref0 ),( PAP

and one has to apply equation (AFIII-19b)

2

10726031397202739.9

10)54744213131272.6354943976950.47(54943976950.47),(

AAP


34.33112094537867

47.49439769505

63.42131312725474 47.49439769505

2)1080(17.7864978 950547.4943976),( AAhP

2)108591(21.5207848 950547.4943976),( AAP



50

Height and Mass Recommendations

Table AFIII-15. Computation of percentiles of height and mass for the next 6 monthsЯ

Dates of

Recommendation

Decimal Age, iA

(years) ),( iAhP ),( iAP

2011-12-13 9.2219178082191781 36.7262402695722 60.52333690133979

2012-01-13 9.3065200239538890 38.9406133662815 57.84405470689426

2012-02-13 9.3914514559473015 40.9075002707716 55.46421859457887

2012-03-13 9.4706864286248971 42.5111037707986 53.52393747801466

2012-04-13 9.5553858821768097 43.9783323122061 51.74866333292258

2012-05-13 9.6373530952915638 45.1552459569492 50.32465588926005

To compute decimal age of first recommendation, iA (years), one needs to refer to Table AFIII-2

(page 4).

Decimal Date of First Recommendation 2011-12-13 2011.9506849315068493

Decimal Date of Birth of M. E. (calculated on page 4) 2002.7287671232876712

Decimal Age of First Recommendation 2011.9506849315068493 – 2002.7287671232876712

9.2219178082191781 years

Computation of ),( iAhP for the first entry:

210)-8082191781221917.9(786497880.1754943976950.47),( AhP

36.7262402695722

Computation of ),( iAP for the first entry:

210)-8082191781221917.9(15207848859.2154943976950.47),( AhP

60.52333690133979

__________________________________________

ЯRow separation in this table and Table AFIII-17b as per color scheme given in Table AFIII-20

365

133342011

2)1080(17.7864978950547.4943976),( AAhP

2)108591(21.5207848 950547.4943976),( AAP



51

Table AFIII-16a. Computation of height from percentile of height

using box interpolation (first entry in Table AFII-14)

7227262402695.36)( hP

Percentile

Age (years)

P(h<) = 25 7227262402695.36)( hP P(h>) = 50

A 9.0

128.78195 130.7228538369391

132.91990

A 9.2219178082191781

129.8266502739726 131.7991039298138

131.7991039298138

134.0318635616438

A 9.5

131.13575 133.1477383054532

135.42525

h = 131.7991039298138 cm

Hence, the first recommendation for height of M. E. comes out to 131.7991039298138 cm

Table AFIII-16b. Computation of mass from percentile of mass

using box interpolation (first entry in Table AFII-14)

013397960.5233369)( P

Percentile

Age (years)

P(<) = 50 013397960.5233369)( P P(>) = 75

A 9.0

28.99138 30.7248471944101

33.10953

A 9.2219178082191781

29.82855605479452 31.63757538791696

31.63757538791696

34.12619317808219

A 9.5

30.87761 32.78130269212617

35.40016

= 31.63757538791696 kg

Hence, the first recommendation for mass of M. E. comes out to 31.63757538791696 kg



52

Detailed Calculations of Height from Percentile of Height (first entry in Table AFII-14)

Height is computed through 2 different routes, one along ‘constant-age route’ and the other

along ‘constant-percentile route’, with identical results obtained (Table AFIII-16a; page 51).



(AFIII-20a)

)(,)()(

)()(

recomm.recomm.

recomm.recomm. hPAhAh

AhAh

AA

AAconstant


(AFIII-20b)

)(,)()()()( recomm.recomm.recomm.recomm. hP

AA

AAAhAhAhAh constant



(AFIII-21a)

APhPh

PhPh

PP

PP,

)()(

)()(

recomm.recomm.

recomm.recomm. constant


(AFIII-21b)

A

PP

PPPhPhPhPh ,)()()()( recomm.recomm.recomm.recomm. constant

To evaluate recommended height, ,recomm.h please refer to Table AFIII-16a (page 51) and Table

AFIII-5a: copy (page 13). The ages are A 9.0 years, A 9.5 years. The calculations based on


To evaluate Ph (recomm. 25; A 9.2219178082191781 years) ,1recomm.h one uses

Ph (recomm. 25; A 9.0 years) )(recomm. Ah cm, Ph (recomm. 25; A 9.5

years) )(recomm. Ah cm, in equation (AFIII-18b), constant-percentile route, to get

0.95.9

0.9 821917819.22191780)28.781951131.78195(28.7819511recomm.

h

129.8266502739726 cm

To evaluate Ph (recomm. 50; A 9.2219178082191781 years) ,2recomm.h one uses

Ph (recomm. 50; A 9.0 years) )(recomm. Ah cm, Ph (recomm. 50; A 9.5

years) )(recomm. Ah cm, in equation (AFIII-20b), constant-percentile route, to get

0.95.9

0.9821917819.22191780)132.91990.42525135(132.919902recomm.

h

134.0318635616438 cm

To compute recommended height, ,recomm.h one substitutes P 25, P 36.7262402695722,

P 50, 1recomm.h 129.8266502739726 cm, 2recomm.h 134.0318635616438 cm, in equation

(AFIII-21b), ‘constant-age route’, to obtain

250 5

2569572236.7262402)2739726129.826650 5616438134.031863(2739726129.826650recomm.

h

131.7991039298138 cm, A 9.2219178082191781 years


128.78195

135.42525

132.91990

131.13575



53

To evaluate Ph (recomm. 36.7262402695722; A 9.0.years) ,recomm.Ah one uses Ph (recomm.

25; A 9.0.years) )(recomm. Ph ………...…….cm, Ph (recomm. 50; A 9.0.years)

)(recomm. Ph …………….cm, in equation (AFIII-21b), constant-age route, to get

2550

2569572236.7262402)128.78195132.91990(128.78195recomm.A

h

130.7228538369391 cm

To evaluate recomm.h (P 36.7262402695722; A 9.5.years) ,recomm.Bh one uses Ph (recomm.

25; A 9.5.years) )(recomm. Ph ……..……....cm, Ph (recomm. 50; A 9.5.years)

)(recomm. Ph ……..……..cm, in equation (AFIII-21b), constant-age route, to get

2550

2569572236.7262402)131.13575.42525135(131.13575recomm.B

h

133.1477383054532 cm

To compute recommended height, ,recomm.h one substitutes A 9.0 years, A

, 821917819.22191780 years ,5.9 yearsA recomm.Ah 130.7228538369391 cm, recomm.Bh


0.99.5

0.9 821917819.22191780)8369391130.722853 3054532133.147738( 8369391130.722853recomm.

h

131.7991039298138 cm, P 36.7262402695722

128.78195

132.91990

131.13575

135.42525



54

Detailed Calculations of Mass from Percentile of Mass (first entry in Table AFII-14)

Mass is computed through 2 different routes, one along ‘constant-age route’ and the other

along ‘constant-percentile route’, with identical results obtained (Table AFIII-16b; page 51).



(AFIII-22a)

)(,)()(

)()(

recomm.recomm.

recomm.recomm.

P

AA

AA

AA

AAconstant


(AFIII-22b)

)(,)()()()( recomm.recomm.recomm.recomm. P

AA

AAAAAA constant



(AFIII-23a)

APP

PP

PP

PP,

)()(

)()(

recomm.recomm.

recomm.recomm.

constant


(AFIII-23b)

A

PP

PPPPPP ,)()()()( recomm.recomm.recomm.recomm. constant

To evaluate recommended mass, ,recomm. please refer to Table AFIII-16b (page 51) and Table

AFIII-6c: copy (page 20). The ages are A 9.0 years, A 9.5 years. The calculations based on


To evaluate P(recomm. 50; A 9.2219178082191781 years) ,1recomm. one uses

P(recomm. 50; A 9.0 years) )(recomm. A ……..……..kg, P(recomm. 50; A 9.5

years) )(recomm. A ……………kg, in equation (AFIII-22b), constant-percentile route, to get

0.95.9

0.9 821917819.22191780)28.9913830.87761(28.991381recomm.

29.82855605479452 kg

To evaluate P(recomm. 75; A 9.2219178082191781 years) ,2recomm. one uses

P(recomm. 75; A 9.0 years) )(recomm. A …………..kg, P(recomm. 75; A 9.5

years) )(recomm. A …………..kg, in equation (AFIII-22b), constant-percentile route, to get

0.95.9

0.9821917819.22191780)33.1095335.40016(33.109532recomm.

34.12619317808219 kg

To compute recommended mass, ,recomm. one substitutes P 50, P 60.52333690133979,

P 75; 1recomm. 29.82855605479452 kg, 2recomm. 34.12619317808219 kg, in equation

(AFIII-23b), ‘constant-age route’, to obtain

28.99138

30.87761

33.10953

35.40016



55

50 75

50013397960.5233369)547945229.8285560 780821934.1261931(547945229.8285560recomm.

31.63757538791696 kg, A 9.2219178082191781 years


To evaluate P(recomm. 60.52333690133979; A 9.0.years) ,recomm.A one uses

P(recomm. 50; A 9.0.years) )(recomm. P ……..……kg, P(recomm. 75; A 9.0

.years) )(recomm. P …… …….kg, in equation (AFIII-23b), constant-age route, to get

5075

50013397960.5233369)28.9913833.10953(28.99138recomm.A

30.7248471944101 kg

To evaluate P(recomm. 60.52333690133979; A 9.5.years) ,recomm.B one uses

P(recomm. 50; A 9.5.years) )(recomm. P ………….kg, P(recomm. 75; A 9.5

.years) )(recomm. P …… …….kg, in equation (AFIII-23b), constant-age route, to get

5075

50013397960.5233369)30.8776135.40016(30.87761recomm.B

32.78130269212617 kg

To compute recommended mass, ,recomm. one substitutes A 9.0 years, A

, 821917819.22191780 years ,5.9 yearsA recomm.A 30.7248471944101 kg, recomm.B


0.99.5

0.9 821917819.22191780) 94410130.7248471 921261732.7813026( 94410130.7248471recomm.

31.63757538791696 kg, P 60.52333690133979

28.99138

33.10953

30.87761

35.40016



56

Growth-and-Obesity Vector-Roadmap

Table AFIII-17a. Growth-and-Obesity Vector-Roadmap of M. E. (SGPP-KHI-20100421-03/01)

Gender: Female• Date of Birth (year-month-day): 2002-09-23 • Army-Cutoff Height: 157.48 cm (19.36

P)

Father’s Height:167.80 cm • Mother’s Height:171.00 cm • Target Height: 162.90 cm (47.49P)

Checkup 1st 2

nd

Photograph

Scanned Signatures ME ME

Class IV IV

Date of Checkup (year-month-day) 2011-05-22 2011-11-13

Age (year-month-day) 08-07-29 09-01-20

Age (decimal years) 8.66 9.14

Dress Code 0/0.5 0/0.5

Behavior Code 0 0

Height, h (cm) 129.50 131.00

Height (ft-in) 4 ft 2.98 in 4 ft 3.57 in

Percentile-of-Height, P(h) 39.73 34.33

Estimated-Adult Height (cm) 161.54 160.60

Estimated-Adult Height (ft–in) 5 ft 3.60 in 5 ft 11.01 in

CA-MP (Current-Age-Mid-Parental) Height (cm) 130.76 133.20

Height w. r. t. CA-MP Height (cm) –1.26 –2.20

CA-AC (Current-Age-Army-Cutoff) Height (cm) 125.78 128.06

Height w. r. t. CA-AC Height (cm) +3.72 +2.94

Reference Height (cm) 130.76 133.20

Percentile-of-Reference-Height, Pref 47.49 47.49

Algebraic Status (pertaining-to-height), STATUS(h) –0.96% –1.65%

Qualitative Status (pertaining-to-height) Normal 1st-Deg Stunted

Gross Mass (kg) 31.90 31.79

Clothing Correction (kg) 0 0

Net Mass, (kg) 31.90 31.79

Net Weight (lb-oz) 70 lb 5.43 oz 70 lb 1.55 oz

Percentile-of-Net-Mass, P() 75.79 63.42

Estimated-Adult Mass (kg) 66.35 62.32 Estimated-Adult Weight (lb–oz) 146 lb 4.86 oz 137 lb 6.54 oz

Height-Percentile-based-Optimal Mass, opt (kg) 26.57 27.45

Mass-for-Height (kg) +5.33 +4.34

Percentile-of-BMI-based-Optimal-Mass, P(BMI) 64.46 62.05

BMI-based-Optimal-Mass, BMI (kg) 30.03 31.56

Algebraic Status (pertaining-to-mass), STATUS() +20.08% +15.82%

Qualitative Status (pertaining-to-mass) 3rd-Deg Obese. 2nd-Deg Obese

Estimated-Adult BMI (kg/m2) 25.43 24.16

Nutritional Status EC II EC II

P(h) + P() 115.51 97.76

Build Medium Medium



57

Table AFIII-17b. Month-wise-targets determined using Growth-and-Obesity

Vector-Roadmap for M. E. based on her most-recent checkup

Target Date Height Target... Mass Target

cm ft-in kg lb-oz

December 13, 2011 131.80 4 ft 3.89 in 31.64 69 lb 12.17 oz

January 13, 2012 132.59 4 ft 4.20 in 31.52 69 lb 7.93 oz

February 13, 2012 133.33 4 ft 4.49 in 31.44 69 lb 5.11 oz

March 13, 2012 134.00 4 ft 4.75 in 31.40 69 lb 3.83 oz

April 13, 2012 134.67 4 ft 5.02 in 31.42 69 lb 4.51 oz

May 13, 2012 135.29 4 ft 5.26 in 31.49 69 lb 7.00 oz



58

Color Scheme of Growth-and-Obesity Vector-Roadmap

Table AFIII-18a. Row separation for different sections of Growth-and-Obesity Vector-Roadmap

Dark green arrows point to color scheme used in Growth-and-Obesity Vector-Roadmaps

inserted in journal paper (without row separation)

Vital Statistics

Light Hue

Sat

Lum

042 255

255 255

204 153

Red

Green

Blue

Dark Hue

Sat

Lum

042 255

255 255

169 083

Red

Green

Blue

Height Data

Light Hue

Sat

Lum

149 189

255 222

222 255

Red

Green

Blue

Dark Hue

Sat

Lum

149 153

255 204

204 255

Red

Green

Blue

Mass Data

Light Hue

Sat

Lum

234 255

255 153

204 204

Red

Green

Blue

Dark Hue

Sat

Lum

234 255

255 117

186 186

Red

Green

Blue

Combined Data

Light Hue

Sat

Lum

085 204

255 255

230 204

Red

Green

Blue

Dark Hue

Sat

Lum

085 129

255 255

192 129

Red

Green

Blue

Table AFIII-18b. Eistimated-adult height <: Lesser than Army-Cutoff Height • >: In Excess of Army-Cutoff Height

Army-Cutoff Height for the Pakistani Youth: 5 feet 4 inches for males and 5 feet 2 inches for females

< Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue

> Hue

Sat

Lum

106 051

128 153

102 102

Red

Green

Blue

Table AFIII-18c. Classification of build

0 PScaled(h) + PScaled() < 50

Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue

Small


Hue

Sat

Lum

104 000

255 176

088 080

Red

Green

Blue

Medium


Hue

Sat

Lum

042 255

255 255

128 000

Red

Green

Blue

Big



59

Tables AFIII-19a, b. Statuses (pertaining-to-height) and (pertaining-to-height)

4th

-Degree Stunted Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue STATUS(h) < –30

3rd

-Degree Stunted Hue

Sat

Lum

019 227

233 108

119 010

Red

Green

Blue –30% STATUS(h) < –20%

2nd

-Degree Stunted Hue

Sat

Lum

032 255

255 192

128 000

Red

Green


1st-Degree Stunted

Hue

Sat

Lum

042 255

255 255

128 000

Red

Green


Normal Hue

Sat

Lum

104 000

255 176

088 080

Red

Green

Blue –1%STATUS(h) < +1%

1st-Degree Tall

Hue

Sat

Lum

042 255

255 255

128 000

Red

Green

Blue +1% STATUS(h) < +10%

2nd

-Degree Tall Hue

Sat

Lum

032 255

255 192

128 000

Red

Green


3rd

-Degree Tall Hue

Sat

Lum

019 227

233 108

119 010

Red

Green


4th

-Degree Tall Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue STATUS(h) +30%

4th

-Degree Wasted Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue STATUS() < –30

3rd

-Degree Wasted Hue

Sat

Lum

019 227

233 108

119 010

Red

Green

Blue –30% STATUS() < –20%

2nd

-Degree Wasted Hue

Sat

Lum

032 255

255 192

128 000

Red

Green


1st-Degree Wasted

Hue

Sat

Lum

042 255

255 255

128 000

Red

Green


Normal Hue

Sat

Lum

104 000

255 176

088 080

Red

Green

Blue –1%STATUS() < +1%

1st-Degree Obese

Hue

Sat

Lum

104 000

255 176

088 080

Red

Green

Blue +1% STATUS() < +10%

2nd

-Degree Obese Hue

Sat

Lum

032 255

255 192

128 000

Red

Green


3rd

-Degree Obese Hue

Sat

Lum

019 227

233 108

119 010

Red

Green


4th

-Degree Obese Hue

Sat

Lum

000 255

255 000

128 000

Red

Green

Blue STATUS() +30%

Table AFIII-20. Row separation in height and mass recommendations

White Hue

Sat

Lum

170 255

000 255

255 255

Red

Green

Blue

Grey Hue

Sat

Lum

170 230

000 230

230 230

Red

Green

Blue



60

Energy-Channelization (EC III) Hue 000 128 Red

Sat 255 000 Green

Lum 064 000 Blue

Energy-Channelization (EC I) Hue 170 000 Red

Sat 255 000 Green

Lum 064 128 Blue

Over-Nutrition (ON)

Hue 085 000 Red

Sat 255 051 Green

Lum 026 000 Blue

Under-Nutrition (UN) Hue 170 051 Red

Sat 000 051 Green

Lum 051 051 Blue

Energy-Channelization (EC II) Hue 213 128 Red

Sat 255 000 Green

Lum 064 128 Blue

Acute Malnutrition (AM) Hue 000 212 Red

Sat 255 000 Green

Lum 106 000 Blue

Fig. AFIII-1. Classification of nutritional status (coördinate-plane representation)

Fig. AFIII-2. Classification of nutritional status (Venn-diagrammic representation)



61

References

Kamal, S. A. (2006, May 23). Manual for Obtaining Anthropometric Measurements. University of

Karachi, Karachi, Pakistan, version 9.1 (release date: April 5, 2016), full text:

https://www.ngds-ku.org/ngds_folder/M02.pdf

Kamal, S. A., N. Jamil and S. A. Khan (2011). Growth-and-Obesity Profiles of children of

Karachi using box-interpolation method. International Journal of Biology and Biotechnology, 8

(1): 87-96, full text: https://www.ngds-ku.org/Papers/J29.pdf

Kamal, S. A. and S. S. Jamil (2012). A method to generate Growth-and-Obesity Profiles of still-

growing parents. International Journal of Biology and Biotechnology, 9 (3): 233-255, full text:


Kamal, S. A. and S. S. Jamil (2014). KJ-regression model to evaluate optimal masses of extreme

cases. International Journal of Biology and Biotechnology, 11 (4): 623-648, full text:


Additional File 3: https://www.ngds-ku.org/Papers/J34/Additional_File_3.pdf

Web address of the main document:

POSSIBLE VALIDATION OF MATHEMATICAL DEFINITION OF CHILDHOOD OBESITY BASED ON

ANTHROPOMETRIC DATA COLLECTED DURING 1998-2013


Web address of this document:

Additional File 3:

DETAILED CALCULATIONS OF M. E.’s GROWTH-AND-OBESITY VECTOR-ROADMAP

https://www.ngds-ku.org/Papers/J46/Additional_File_3.pdf

Table of Contents · Age Computation 04 Boys’ CDC Height Tables 05 Boys’ CDC Mass Tables 08...

Documents

Transcript of Table of Contents · Age Computation 04 Boys’ CDC Height Tables 05 Boys’ CDC Mass Tables 08...