Methods of Organizing Data

Training Course on Basic Statistics for Research

August 24-28, 2009

STATISTICAL RESEARCH AND TRAINING CENTERJ and S Building, 104 Kalayaan Avenue, Diliman, Quezon City

Methods of Organizing Data

Prepared by:Josefina V. AlmedaProfessor and College SecretarySchool of StatisticsUniversity of the Philippines, DilimanAugust 2009

2

Statistical Research and Training Center Training Course on Basic Statistics for ResearchAugust 24 - 28, 2009

Quantitative Classification of Data

* use quantitative classification if the observed values of the data are either a result of count or measurement

* organize this type of data in tabular form in the form of a frequency distribution table.

Frequency distribution is a summarized table wherein theclasses are either distinct values or intervals with a frequencycount.

3


Forms of the Frequency Distribution

Single value grouping* is a frequency count of observed values wherein classes are

distinct values

* range of values is short and with many unique values occurring more than once

Grouping by class intervals* is a frequency count of observed values wherein the classes

are intervals.

4


Data for Single Value Grouping

Suppose we have data on the number of children of 50 currently married women using any modern contraceptive method. Construct a summary table for the data set below.

0 0 1 2 2 2 3 3 4 4

0 0 1 2 2 3 3 3 4 4

0 1 1 2 2 3 3 3 4 4

0 1 1 2 2 3 3 3 4 5

0 1 1 2 2 3 3 3 4 5

5


Example of Single Value Grouping

Distribution of Currently Married Women Using Any Modern Method of Contraceptive by Number of Children:

No. of Frequency of Children Married Women % 0 7 14

1 8 16 2 11 22 3 14 28

4 8 16 5 2 4

TOTAL 50 100

6


Definition of Terms Used in a Frequency Distribution Table

Class interval contains the numbers defining a class.

Class frequency is the number of observations falling under a class interval.

Class limits are the end numbers of a class interval.* The lower class limit (LCL) is the lower end of the class

interval and the upper class limit (UCL) is the upper end of the class interval.

* The number of digits of the class limits should be the same as the number of digits of the raw data.

Open class interval is a class interval with either no lower class limit or upper class limit.

7


Class boundaries are the true class limits.

* There are no gaps in the class boundaries.* The number of decimal places is one more than the

number of decimal place of the class limits.* The lower class boundary (LCB) is average of the

lower class limit of the class interval and the upper class limit of the preceding class interval.

* The upper class boundary (UCB) is the average of the upper class limit of the class interval and the lower class limit of the next class interval.

8


Class size is the size of the class interval. * It is the difference between two successive lower class limits, or two successive upper class limits, or two successive lower class boundaries, or two successive upper class boundaries.

Class mark is the midpoint of a class interval.* It is the average of the lower class limit and the upper

class limit or the average of the lower class boundary and upper class boundary of a class interval.

Modal class is the class interval having the highest frequency.

9


Steps in Constructing a Frequency Distribution Table

1. Determine an adequate number of classes (K).* The number of classes should not be too many or not

too few.* Usually, the number of classes is between 5 and 20.* The class intervals should be non-overlapping.

2. Determine the range (R). Range = Maximum – Minimum

3. Calculate the approximate class size (C’). C’ = R/K

4. Determine the class size (C ) by rounding off C’ to a number that is easy to work with. We recommend class sizes of multiples of 5, 10, 15, 20, etc.

10


5. List the required number (K) of class intervals.

* Start with the lower class limit of the lowest class interval.

* Its value should be less or equal to the minimum value of the data set. * Add the class size (C) to the lower class limit to get

the next lower class limit.* The last class interval should include the maximum

value. 6. Tally the frequency for each class interval.

7. Sum the frequency column and check against the total number of observations.

11


TABLE 3. Magnitude of Poor Population in the Philippines: 2000

NCR 848,962 Region 2 820,786 Region 4a 1,699,333

(National 1st District 120,663 (Cagayan Batanes 2,535 (CALABARZON) Batangas 440,603

Capital 2nd District 229,301 Valley) Cagayan 251,222 Cavite 244,712

Region)1 3rd District 292,611 Isabela 424,580 Laguna 207,184

4th District 206,387 Nueva Vizcaya 82,895 Quezon 667,385

CAR 536,169 Quirino 59,555 Rizal 139,449

(Cordillera Abra 110,937 Region 3 1,695,227 Region 4b 1,030,987

Administrative Apayao 28,770 (Central Aurora 59,985 (MIMAROPA) Marinduque 113,553

Region) Benguet 122,762 Luzon) Bataan 68,659 Occidental Mindoro 177,823

Ifugao 113,719 Bulacan 147,812 Oriental Mindoro 340,690

Kalinga 83,844 Nueva Ecija 532,961 Region 5 2,540,618

Mt. Province 76,137 Pampanga 331,739 (Bicol Albay 553,629

Region 1 1,447,638 Tarlac 360,109 Region) Camarines Norte 301,147

(Ilocos Ilocos Norte 115,116 Zambales 193,962 Camarines Sur 765,373

Region) Ilocos Sur 190,297 Catanduanes 116,866

La Union 253,382 Masbate 483,651

Pangasinan 888,844 Sorsogon 319,952

12


Region 6 2,765,055 Region 8 1,646,371 Region 10 1,580,249

(Western Aklan 186,813 (Eastern Biliran 58,135 (Northern Bukidnon 449,647

Visayas) Antique 208,169 Visayas)Eastern Samar 202,680 Mindanao) Camiguin 41,017

Capiz 328,635 Leyte 680,536 Lanao Del Norte 424,819

Guimaras 37,838Northern Samar 240,228

Misamis Occidental 260,764

Iloilo 690,639 Southern Samar 116,738

Misamis Oriental 404,002

Negros Occidental 1,312,961

Western Samar 348,054 Region 11 1,222,367

Region 7 2,017,162 Region 9 1,254,884 (DavaoDavao del Norte 637,298

(Central Bohol 590,926 (ZamboangaZamboanga del Norte 433,091 Region) Daval del Sur 412,442

Visayas) Cebu 973,490 Peninsula)Zamboanga del Sur 821,793

Davao Oriental 172,627

Negros Oriental 427,509

Zamboanga 2 Sibugay

Compostela 4 Valley

Siquijor 25,237 Isabela City3

13


Region 12 1,596,785 Region 13 1,071,005 ARMM 1,648,441

(SOCCSKSARGEN) North Cotabato 509,463 (Caraga) Agusan del Norte 259,475

(Autonomous Region Basilan 123,825

Saranggani 223,279 Agusan del Sur 353,825in Muslim Mindanao

Lanao del Sur 432,307

South Cotabato 469,874 Surigao del Norte 232,065 Maguindanao 534,628

Sultan Kudarat 344,172 Sulu 397,119

Cotabato City 49,997 Tawi-tawi 160,562

1 Districts of NCR cover the following: 1st District – Manila; end District – Mandaluyong, Marikina, Pasig, Quezon City and San Juan; 3rd District - Valenzuela, Kaloocan City, Malabon and Navotas; and 4th District – Las Pinas, Makati, Muntinlupa, Paranaque, Pasay City, Pateros, and Taguig.2 Zamboanga Sibugay was part of Zamboanga del Sur in 2000. Thus, 2000 estimates of Zamboanga del Sur includes Zamboanga Sibugay3 Isabela City was part of Basilan in 2000. Thus, 2000 estimates of Basilan still includes Isabela City.4 Davao del Norte estimates for 2000 include Compostela Valley.Source: National Statistical Coordination Board

14


TABLE 4. Sorted Data (Array) of Magnitude of Poor Population for the 82 provinces of the Philippines: 2000

2,535 76,137 122,762 193,962 240,228 331,739 424,819 534,628 973,490

25,237 82,895 123,825 202,680 244,712 340,690 427,509 553,629 1,312,961

28,770 83,844 139,449 206,387 251,222 344,172 432,307 590,926

37,838 110,937 147,812 207,184 253,382 348,054 433,091 637,298

41,017 113,553 160,562 208,169 259,475 353,825 440,603 667,385

49,997 113,719 170,917 223,279 260,764 360,109 449,647 680,536

58,135 115,116 172,627 225,640 292,611 397,119 469,874 690,639

59,555 116,738 177,823 228,004 301,147 404,002 483,651 765,373

59,985 116,866 186,813 229,301 319,952 412,442 509,463 821,793

68,659 120,663 190,297 232,065 328,635 424,580 532,961 888,844

15


TABLE 5. Frequency Distribution Table on Magnitude of Poor Population for the 82 Provinces of the Philippines: 2000

TABLE 5a

CLASS LIMITS

LCL UCL f

2,500 152,499 24

152,500 302,499 24

302,500 452,499 18

452,500 602,499 7

602,500 752,499 4

752,500 902,499 3

902,500 1,052,499 1

1,052,500 1,202,499 0

1,202,500 1,352,499 1

82

TABLE 5b

CLASS LIMITS

LCL UCL f

2,500 202,499 31

202,500 402,499 26

402,500 602,499 16

602,500 802,499 5

802,500 1,002,499 3

1,002,500 1,202,499 0

1,202,500 1,402,499 1

82

16


TABLE 5c

CLASS LIMITS

LCL UCL f

2,500 192,499 30

192,500 382,499 26

382,500 572,499 16

572,500 762,499 5

762,500 952,499 3

952,500 1,142,499 1

1,142,500 1,332,499 1

82

17


Example: This illustrates the use of appropriate column labels in a frequency distribution table.

TABLE 6. Frequency Distribution Table of the Magnitude of Poor Population in the Phils: 2000

Magnitude of Poor Population No. of Provinces

2,500 - 192,499 30

192,500 - 382,499 26

382,500 - 572,499 16

572,500 - 762,499 5

762,500 - 952,499 3

952,500 - 1,142,499 1

1,142,500 - 1,332,499 1

Total 82

18


TABLE 7. Frequency Distribution Table with Class Boundaries and Class Marks

Class Limits Class Boundaries

LCL UCL LCB UCB Class Mark f

2,500 - 192,499 2,500 - 192,499 97,500 30

192,500 - 382,499 192,500 - 382,499 287,500 26

382,500 - 572,499 382,500 - 572,499 477,500 16

572,500 - 762,499 572,500 - 762,499 667,500 5

762,500 - 952,499 762,500 - 952,499 857,500 3

952,500 - 1,142,499 952,500 - 1,142,499 1,047,500 1

1,142,500 - 1,332,499 1,142,500 - 1,332,499 1,237,500 1

82

19


Relative Frequency and Relative Frequency Percentage

Relative frequency* divide the class frequency of a class interval to the number of observations* the sum of the relative frequency column is one

Relative frequency percentage* multiply the relative frequency by 100* the sum of the relative frequency percentage column is one hundred percent.

20


TABLE 8. Frequency Distribution Table with Relative Frequency and Relative

Frequency Percentage

Relative

Class Limits Relative Frequency

LCL UCL f Frequency Percentage

2,500 - 192,499 30 0.366 36.6

192,500 - 382,499 26 0.317 31.7

382,500 - 572,499 16 0.195 19.5

572,500 - 762,499 5 0.061 6.1

762,500 - 952,499 3 0.037 3.7

952,500 -1,142,499 1 0.012 1.2

1,142,500 -1,332,499 1 0.012 1.2

82 1.000 100.0

21


TABLE 9. Frequency Distribution Table with Less than Cumulative Frequency and Greater than

Cumulative Frequency Distributions

Class Limits Less than

cumulative

Greater than Cumulative Frequency

LCL UCL f Frequency

2,500 - 192,499 30 30 82

192,500 - 382,499 26 56 52

382,500 - 572,499 16 72 26

572,500 - 762,499 5 77 10

762,500 - 952,499 3 80 5

952,500 -1,142,499 1 81 2

1,142,500 -1,332,499 1 82 1

82

22


Graphical Representation of the Frequency Distribution

Frequency Histogram

- use the class frequency on the vertical axis and the class boundaries on the horizontal axis

Frequency Polygon

- use the class frequency on the vertical axis and the class mark on the horizontal axis

Training Course on Basic Statistics for Research

August 24-28, 2009

STATISTICAL RESEARCH AND TRAINING CENTERJ and S Building, 104 Kalayaan Avenue, Diliman, Quezon City

Thank you.

Methods of Organizing Data

Documents

Transcript of Methods of Organizing Data