Statistic Addmath Project

7/28/2019 Statistic Addmath Project

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Additional

MathematicsProject Work 2013

Name :

Class :

IC number :

Title :


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Contents..

Subtitles Page

i) Appreciationii) Objectivesiii) Moral and Esthetic Valuesiv) Historyv) Introductionvi) Questionvii) Task Specificationviii) Problem Solvingix) Findingsx) Further Explorationxi) Conclusionxii) Referencexiii) Rubic


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Moral and esthetic

values..


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Objectives..We students taking Additional Mathematics are required to carry out a project work while weare in Form 5. This year the Curriculum Development Division, Ministry of Education has

prepared task for us. We need to choose and complete only one task based on our interest.

This project can be done in group or individually. Upon completion of the Additional

Mathematics project work, we can gain valuables experience and able to:

Apply and adopt a variety of problem solving strategies to solve routines and non-

routine problems.

Improve our thinking skills.

Knowledge and skills are applied in meaningful ways in solving real-life problems.

Expressing ones mathematical thinking, reasoning and communication are highly

encouraged and expected.Stimulate and enhances effective learning.

Acquire effective mathematical communication through oral and writing and to use

the language of mathematics to express mathematical ideas correctly and precisely.

Enhance acquisition of mathematical knowledge and skills through problem-solving in

way that increase interest and confidence.

Prepare ourselves for the demand of our future undertakings and in workplace.

Realize that mathematics is an important and powerful tool in solving real life

problems and hence develop positive attitude toward mathematics.

Train ourselves not only to be independent learners but also to collaborate to cooperate

and to share knowledge in an engaging and healthy environment.

Use technology especially the ICT appropriately and effectively.

Train ourselves to appreciate the intrinsic value of mathematics and to become more

creative and innovative.

Realize the important and beauty of mathematics

We are expected to submit the project work within three weeks for the first day the task is

being admixture to us.


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History ..The History of statistics can be said to start around 1749 although, over time, there

have been changes to the interpretation of the wordstatistics. In early times, the meaning was

restricted to information about states. This was later extended to include all collections of

information of all types, and later still it was extended to include the analysis and

interpretation of such data. In modern terms, "statistics" means both sets of collected

information, as in national accounts and temperature records, and analytical work which

requires statistical inference.

Statistical activities are often associated with models expressed using probabilities,

and require probability theory for them to be put on a firm theoretical basis: see History of

probability.

A number of statistical concepts have had an important impact on a wide range of

sciences. These include the design of experiments and approaches to statistical inference such

as Bayesian inference, each of which can be considered to have their own sequence in the

development of the ideas underlying modern statistics.

Statistics Today

Statistics is the study of the collection, organization, analysis, and interpretation of

data. It deals with all aspects of this, including the planning of data collection in terms of the

design ofsurveys and experiments.

The word statistics, when referring to the scientific discipline, is singular, as in

"Statistics is an art." This should not be confused with the word statistic, referring to aquantity (such as mean or median) calculated from a set of data, whose plural is statistics

("this statistic seems wrong" or "these statistics are misleading").

The earliest writing on statistics was found in a 9th century book entitled: "Manuscripton Deciphering Cryptographic Messages", written by Al-Kindi (801873 CE). In his book,

Al-Kindi gave a detailed description of how to use statistics and frequency analysis to

decipher encrypted messages, this was the birth of both statistics and cryptanalysis, according

to Ibrahim Al-Kadi.

Some scholars pinpoint the origin of statistics to 1663, with the publication ofNatural

and Political Observations upon the Bills of Mortality by John Graunt. Early applications of

statistical thinking revolved around the needs of states to base policy on demographic and

economic data, hence its stat- etymology. The scope of the discipline of statistics broadened

in the early 19th century to include the collection and analysis of data in general. Today,

statistics is widely employed in government, business, and the natural and social sciences.
http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Theory_%28mathematical_logic%29http://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Statistical_surveyhttp://en.wikipedia.org/wiki/Experimental_designhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Medianhttp://en.wikipedia.org/wiki/Al-Kindihttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/History_of_statistics#Etymologyhttp://en.wikipedia.org/wiki/History_of_statistics#Etymologyhttp://en.wikipedia.org/wiki/History_of_statistics#Etymologyhttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/Al-Kindihttp://en.wikipedia.org/wiki/Medianhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Experimental_designhttp://en.wikipedia.org/wiki/Statistical_surveyhttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Bayesian_inferencehttp://en.wikipedia.org/wiki/Design_of_experimentshttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/History_of_probabilityhttp://en.wikipedia.org/wiki/Theory_%28mathematical_logic%29http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Statistical_inferencehttp://en.wikipedia.org/wiki/Temperature_recordhttp://en.wikipedia.org/wiki/National_accountshttp://en.wikipedia.org/wiki/Sovereign_statehttp://en.wikipedia.org/wiki/Statistics


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Its mathematical foundations were laid in the 17th century with the development of

probability theoryby Blaise Pascal and Pierre de Fermat. Probability theory arose from the

study of games of chance. The method of least squares was first described by Carl Friedrich

Gauss around 1794. The use of modern computers has expedited large-scale statistical

computation, and has also made possible new methods that are impractical to perform

manually.
http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Blaise_Pascalhttp://en.wikipedia.org/wiki/Pierre_de_Fermathttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Computerhttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Method_of_least_squareshttp://en.wikipedia.org/wiki/Pierre_de_Fermathttp://en.wikipedia.org/wiki/Blaise_Pascalhttp://en.wikipedia.org/wiki/Probability_theory


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Introduction..

Obesity is a medical condition in which excess body fat has accumulated to the extent

that it may have an adverse effect on health, leading to reduced life expectancy and/or

increased health problems. People are considered obese when theirbody mass index(BMI), a

measurement obtained by dividing a person's weight in kilogramsby the square of the

person's height in metres, exceeds 30 kg/m2.

Obesity increases the likelihood ofvarious diseases, particularly heart disease, type 2

diabetes, obstructive sleep apnea, certain types ofcancer, and osteoarthritis. Obesity is mostcommonly caused by a combination of excessive food energy intake, lack of physical activity,

and genetic susceptibility, although a few cases are caused primarily by

genes, endocrine disorders, medications orpsychiatric illness. Evidence to support the view

that some obese people eat little yet gain weight due to a slow metabolism is limited; on

average obese people have a greater energy expenditure than their thin counterparts due to the

energy required to maintain an increased body mass.

Dieting and physical exercise are the mainstays of treatment for obesity. Diet quality

can be improved by reducing the consumption of energy-dense foods such as those high in fat

and sugars, and by increasing the intake ofdietary fiber. Anti-obesity drugs may be taken to

reduce appetite or inhibit fat absorption together with a suitable diet. If diet, exercise and

medication are not effective, a gastric balloon may assist with weight loss, orsurgery may be

performed to reduce stomach volume and/or bowel length, leading to earliersatiationand

reduced ability to absorb nutrients from food.

Obesity is a leading preventable cause of death worldwide, with

increasing prevalence in adults and children, and authorities view it as one of the most

serious public healthproblems of the 21st century. Obesity is stigmatized in much of the

modern world (particularly in the Western world), though it was widely perceived as a symbol

of wealth and fertility at other times in history, and still is in some parts of the world. In 2013,

the American Medical Association classified obesity as a disease.
http://en.wikipedia.org/wiki/Medical_conditionhttp://en.wikipedia.org/wiki/Body_fathttp://en.wikipedia.org/wiki/Life_expectancyhttp://en.wikipedia.org/wiki/Body_mass_indexhttp://en.wikipedia.org/wiki/Kilogramshttp://en.wikipedia.org/wiki/Metreshttp://en.wikipedia.org/wiki/Obesity-associated_morbidityhttp://en.wikipedia.org/wiki/Cardiovascular_diseaseshttp://en.wikipedia.org/wiki/Diabetes_mellitus_type_2http://en.wikipedia.org/wiki/Diabetes_mellitus_type_2http://en.wikipedia.org/wiki/Obstructive_sleep_apneahttp://en.wikipedia.org/wiki/Cancerhttp://en.wikipedia.org/wiki/Osteoarthritishttp://en.wikipedia.org/wiki/Food_energyhttp://en.wikipedia.org/wiki/Polygenic_inheritancehttp://en.wikipedia.org/wiki/Genehttp://en.wikipedia.org/wiki/Endocrinehttp://en.wikipedia.org/wiki/Medicationhttp://en.wikipedia.org/wiki/Psychiatric_illnesshttp://en.wikipedia.org/wiki/Dietinghttp://en.wikipedia.org/wiki/Physical_exercisehttp://en.wikipedia.org/wiki/Dietary_fiberhttp://en.wikipedia.org/wiki/Anti-obesity_drughttp://en.wikipedia.org/wiki/Gastric_balloonhttp://en.wikipedia.org/wiki/Bariatric_surgeryhttp://en.wikipedia.org/wiki/Satiationhttp://en.wikipedia.org/wiki/Preventable_causes_of_deathhttp://en.wikipedia.org/wiki/Prevalencehttp://en.wikipedia.org/wiki/Childhood_obesityhttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Weight_stigmahttp://en.wikipedia.org/wiki/Western_worldhttp://en.wikipedia.org/wiki/American_Medical_Associationhttp://en.wikipedia.org/wiki/American_Medical_Associationhttp://en.wikipedia.org/wiki/Western_worldhttp://en.wikipedia.org/wiki/Weight_stigmahttp://en.wikipedia.org/wiki/Public_healthhttp://en.wikipedia.org/wiki/Childhood_obesityhttp://en.wikipedia.org/wiki/Prevalencehttp://en.wikipedia.org/wiki/Preventable_causes_of_deathhttp://en.wikipedia.org/wiki/Satiationhttp://en.wikipedia.org/wiki/Bariatric_surgeryhttp://en.wikipedia.org/wiki/Gastric_balloonhttp://en.wikipedia.org/wiki/Anti-obesity_drughttp://en.wikipedia.org/wiki/Dietary_fiberhttp://en.wikipedia.org/wiki/Physical_exercisehttp://en.wikipedia.org/wiki/Dietinghttp://en.wikipedia.org/wiki/Psychiatric_illnesshttp://en.wikipedia.org/wiki/Medicationhttp://en.wikipedia.org/wiki/Endocrinehttp://en.wikipedia.org/wiki/Genehttp://en.wikipedia.org/wiki/Polygenic_inheritancehttp://en.wikipedia.org/wiki/Food_energyhttp://en.wikipedia.org/wiki/Osteoarthritishttp://en.wikipedia.org/wiki/Cancerhttp://en.wikipedia.org/wiki/Obstructive_sleep_apneahttp://en.wikipedia.org/wiki/Diabetes_mellitus_type_2http://en.wikipedia.org/wiki/Diabetes_mellitus_type_2http://en.wikipedia.org/wiki/Cardiovascular_diseaseshttp://en.wikipedia.org/wiki/Obesity-associated_morbidityhttp://en.wikipedia.org/wiki/Metreshttp://en.wikipedia.org/wiki/Kilogramshttp://en.wikipedia.org/wiki/Body_mass_indexhttp://en.wikipedia.org/wiki/Life_expectancyhttp://en.wikipedia.org/wiki/Body_fathttp://en.wikipedia.org/wiki/Medical_condition


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Question ..


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Task Specification..Obesity is a medical condition in which excess body fat has accumulated to the extent that it

may have an adverse effect on health, leading to reduced life expectancy or increased health

problems.

Science club in your school intends to carry out a study on the ideal body fat percentage in

human body. As the president of the Science club, you are required to collect data randomly

which consists of 40 students (below 20 years old) and 40 adults (20-55 years old). It is

advisable to use equal number of males and females for each category.

PART 1

a) Compile your data by using the following format.Respondent Gender Height(m) Weight(kg) Age(years)

1

2

80

b) By using at least two methods , find the mean, mode, median, range, interquartilerange, variance and standard deviation for the weights of thge respondents in the form

of ungrouped data.

( without considering the age and gender of the respondents )


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PART 2

Construct a frequency table for the grouped data for the weights obtained in ascending or

descending order.

Class interval Tally Midpoint, x Frequency, f

a) Represent your data from the frequency distributiontable by using three differentstatistical graphs. Hence,

i) Estimate the modeii) Find the median and interquartile range of the weight of the respondents.

b) Calculate(i)the mean, mode and median,

(ii)Range, interquartile range and standard deviation, for the weights of the

respondents.

Compare and comment the answers of Part 1 and Part 2.

PART 3

Based on your answers in Part 1 and Part 2, determine the measurements of central tendency

(mean, mode, and median ) or measurements of dispersion (range, interquartile range,

variance and standard deviation) which will be your most suitable choice to represent the

weights of the respondents. Give your reason.


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Further exploration...

The amount of body fat, your body fat percentage, makes s difference to your body shape and

your health. Most sources agree that the human body requires a certain amount of fat for good

health. Fat helps to regulate body temperature, store nergy, cushion and insulate organs. The

following table describes body fat ranges and their associated categories.

General Body Fat Percentage Categori es

Description Male Female

Essential Fat 3-4 % 11-14%

Athletes 5-11% 15-18%

Normal 12-18% 19-24%

Overweight 19-24% 26-31%

Obese >24% >31%

Formulae to calculate the body fat percentage.

% of Body Fat for Children*=(1.51x BMI)(0.70 x Age )-(3.6 x Gender **)+1.4

% of Body Fat for Adult* =(1.20x BMI)(0.23x Age)- (10.8x Gender**) +5.4

Notes:

BMI *Children = Aged 19 years and below

*Adult-Aged 20 years and above**Male= 1

**Female= 0


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a) Calculate the body fat percentage for each and every respondent.b) Based on the information given and data collected, determined the percentage

of respondents that are athletes and obese. Represent your finding using

statistical graphs.

c) Compare and comment on the relation between(i) Age and body fat percentage(ii) Gender and body fat percentage

d) Suggest ways to help a person to achieve and maintain a healthy life dependingon body fat percentage. (Find the information from the internet and state the

website address in your bibliography.)

REFLECTION

While you were conducting the project, what have you learnt? What moral values didi you

practise? Represent your opinions or feelings creatively through usage of symbols,

illustrations, drawings or even in a song.


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Problem solving..

Part 1a) DataRespondents Gender Height (m) Weight(kg) Age (years)

1 Female 1.53 51 17

2 Female 1.54 51 17

3 Female 1.51 39 17

4 Female 1.49 42 17

5 Female 1.50 40 16

6 Female 1.55 36 17

7 Female 1.59 56 17

8 Male 1.58 55 179 Male 1.70 78 17

10 Female 1.56 56 17

11 Male 1.60 70 17

12 Female 1.57 52 17

13 Male 1.65 85 17

14 Male 1.63 59 17

15 Female 1.56 41 17

16 Male 1.54 56 17

17 Male 1.76 70 17

18 Male 1.71 48 16

19 Female 1.45 42 1720 Female 1.54 41 17

21 Male 1.67 52 16

22 Male 1.70 53 17

23 Female 1.56 52 18

24 Male 1.68 52 15

25 Female 1.47 45 17

26 Female 1.57 51 17

27 Female 1.51 47 16

28 Male 1.66 52 17

29 Male 1.80 75 17

30 Female 1.49 42 15

31 Male 1.55 54 16

32 Male 1.57 56 17

33 Female 1.67 55 18

34 Male 1.60 50 16

35 Male 1.70 50 16

36 Female 1.50 38 17

37 Female 1.49 40 17

38 Male 1.56 49 17

39 Male 1.53 54 17

40 Male 1.78 58 18

41 Female 1.63 53 38

42 Female 1.45 68 5143 Female 1.50 53 35


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44 Female 1.50 53 22

45 Male 1.66 79 30

46 Male 1.72 51 28

47 Male 1.65 69 28

48 Male 1.77 79 41

49 Male 1.80 58 2050 Male 1.77 65 22

51 Female 1.50 43 39

52 Male 1.61 68 43

53 Female 1.49 60 49

54 Male 1.68 70 50

55 Female 1.58 56 37

56 Male 1.80 75 44

57 Female 1.54 64 22

58 Female 1.63 68 26

59 Female 1.49 55 28

60 Male 1.70 72 43

61 Female 1.50 65 44

62 Male 1.70 60 53

63 Female 1.49 41 48

64 Male 1.75 69 49

65 Female 1.53 55 43

66 Female 1.58 60 21

67 Female 1.49 42 36

68 Male 1.48 52 37

69 Female 1.55 76 33

70 Male 1.60 78 46

71 Male 1.82 67 45

72 Female 1.51 78 3973 Male 1.61 79 49

74 Male 1.72 69 52

75 Female 1.62 57 20

76 Male 1.70 60 25

77 Male 1.80 57 30

78 Female 1.69 74 42

79 Male 1.81 51 30

80 Female 1.63 65 21

51 51 39 42 40 36

56 55 78 56 70 5248 70 56 41 59 8542 41 52 53 52 52

45 51 47 52 75 4254 56 55 50 50 384055785767

4972767860

5452657957

5860426974

5341605751

6869556065

5369

68

6879

64

5358

75

5365

56

7943

70

5168

60


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Method 1

Mean =

80

=

= 57.59

Mode = the most frequently in the data.

= 52

Range = maximum valueminimum value

=8536

=49

Interquartile range =3rd quartile -1st quartile ( ) ( ) Variance = =

(59.05)2= 27899523486.90

= 275,465.30


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Method 2

Mass (x) Frequency (f) x f x

36 1 1296 1296

38 1 1444 1444

39 1 1521 1521

40 2 1600 320041 3 1681 5043

42 4 1764 7056

43 1 1849 1849

45 1 2025 2025

47 1 2209 2209

48 1 2304 2304

49 1 2401 2401

50 2 2500 5000

51 5 2601 13005

52 6 2704 1622453 4 2809 11236

54 2 2916 5832

55 4 3025 12100

56 5 3136 15680

57 2 3249 6498

58 2 3364 6728

59 1 3481 3481

60 4 3600 14400

64 1 4096 4096

65 3 4225 12675

67 1 4489 448968 3 4624 13872

69 3 4761 14283

70 3 4900 14700

72 1 5184 5184

74 1 5476 5476

75 2 5625 11250

76 1 5776 5776

78 3 6084 18252

79 3 6241 18723

85 1 7225 7225f=80 fx =346533


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Mode= the most occur

= 52

Range=85-36

=49


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Part 2

Class Interval Tally Midpoint,x Frequency,f

31-40 IIII 35.5 5

41-50 IIII IIII IIII 45.5 14

51-60 IIII IIII IIII IIII IIII IIII IIII 55.5 3561-70 IIII IIII IIII 65.5 14

71-80 IIII IIII I 75.5 11

81-90 I 85.5 1

a) Histogram graph

i) Mode= 55.5

30.5 40.5 50.560.5 70.5 80.5 90.5

0

5

10

15

20

25

30

35

40

NUmberofrespondents

Mass( kg )


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Frequency polygon graph

Ogive graph

Class interval Upper boundary Frequency Cumulative frequency

21-30 30.5 0 0

31-40 40.5 5 5

41-50 50.5 14 1951-60 60.5 35 54

61-70 70.5 14 68

71-80 80.5 11 79

81-90 90.5 1 80

25.5 35.5 45.5 55.5 65.5 75.5 85.5 95.50

5

10

15

20

25

30

35

40

NUmberofrespondents

weight (kg)

30.5 40.5 50.5 60.5 70.5 80.5 90.50

10

20

30

40

50

60

70

80

90

Numberofrespond

ents

weight(kg)


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( ) ( ) 50.5


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*

+ *

+

* +* +

The value of answers in Part 1 is higher than in part 2. Different formula is used to find mean,

mode, median, range, interquartile range, variance and standard deviation in ungrouped data

and grouped data.


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Part 3


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(a)

Gender Height(m) Weight(kg) Age

(years)

BMI Body Fat

Percentage

(%)

Body Fat

Percentage

Category

Female 1.53 51 17 21.79 22.40 Normal

Female 1.54 51 17 21.50 21.97 Normal

Female 1.51 39 17 17.10 15.32 Athletes

Female 1.49 42 17 18.92 18.07 Athletes

Female 1.50 40 16 17.78 17.07 Athletes

Female 1.55 36 17 14.98 12.12 Essential fat

Female 1.59 56 17 22.15 22.95 Normal

Male 1.58 55 17 22.03 19.17 Overweight

Male 1.70 78 17 26.99 26.65 Obese

Female 1.56 56 17 23.01 24.25 Normal

Male 1.60 70 17 27.34 27.18 Obese

Female 1.57 52 17 21.10 21.36 Normal

Male 1.65 85 17 31.22 33.04 Obese

Male 1.63 59 17 22.21 19.44 Overweight

Female 1.56 41 17 16.85 14.96 Essen

Male 1.54 56 17 23.61 21.55 Overweight

Male 1.76 70 17 22.60 20.03 OverweightMale 1.71 48 16 16.42 11.39 Athletes

Female 1.45 42 17 19.98 19.67 Normal

Female 1.54 41 17 17.29 15.61 Athletes

Male 1.67 52 16 18.65 14.76 Normal

Male 1.70 53 17 18.34 13.61 Normal

Female 1.56 52 18 21.37 21.07 Normal

Male 1.68 52 15 18.42 15.11 Normal

Female 1.47 45 17 20.82 20.94 Normal

Female 1.57 51 17 20.69 20.74 Normal

Female 1.51 47 16 20.61 21.32 Normal

Male 1.66 52 17 18.87 14.39 Normal

Male 1.80 75 17 23.15 20.86 Overweight

Female 1.49 42 15 18.92 19.47 Normal

Male 1.55 54 16 22.48 20.54 Overweight

Male 1.57 56 17 22.72 20.21 Overweight

Female 1.67 55 18 19.72 18.58 Athletes

Male 1.60 50 16 19.53 16.09 Normal

Male 1.70 50 16 17.30 12.75 Normal

Female 1.50 38 17 16.89 15.00 Athletes

Female 1.49 40 17 18.02 16.71 Athletes

Male 1.56 49 17 20.13 16.30 NormalMale 1.53 54 17 23.07 20.74 Overweight


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Male 1.78 58 18 18.31 12.85 Normal

Female 1.63 53 38 19.95 20.60 Normal

Female 1.45 68 51 32.34 30.48 Obese

Female 1.50 53 35 23.56 25.62 Overweight


Male 1.66 79 30 28.67 22.10 OverweightMale 1.72 51 28 17.24 8.85 Athletes

Male 1.65 69 28 25.34 `18.57 Normal

Male 1.77 79 41 25.22 15.43 Normal

Male 1.80 58 20 17.90 11.48 Athletes

Male 1.77 65 22 20.75 14.44 Normal

Female 1.50 43 39 19.11 19.36 Normal

Male 1.61 68 43 26.23 16.19 Normal


Male 1.68 70 50 24.80 12.86 Normal

Female 1.58 56 37 22.43 23.81 NormalMale 1.80 75 44 23.15 12.26 Normal

Female 1.54 64 22 26.99 32.73 Obese



Male 1.70 72 43 24.91 14.60 Normal


Male 1.70 60 53 20.76 7.32 Athletes

Female 1.49 41 48 18.46 16.51 Athletes

Male 1.75 69 49 22.53 10.37 Athletes

Female 1.53 55 43 23.49 23.70 Normal


Female 1.49 42 36 18.92 19.83 Normal

Male 1.48 52 37 23.74 14.58 Normal

Female 1.55 76 33 31.61 35.77 Obese

Male 1.60 78 46 30.47 20.58 Overweight

Male 1.82 67 45 20.23 8.53 Athletes

Female 1.51 78 39 34.21 37.48 Obese

Male 1.61 79 49 30.48 19.91 Overweight

Male 1.72 69 52 23.32 10.62 Athletes


Male 1.70 60 25 20.76 13.76 NormalMale 1.80 57 30 17.59 8.81 Athletes


Male 1.81 51 30 15.56 4.99 Essential fat



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b)Class interval frequency Upper boundary midpoint

1-10 5 10.5 5.5

11-20 11 20.5 15.5

21-30 2 30.5 25.5

31-40 5 40.5 35.5

Histogram Graph

Frequency Polygon Graph

0.5 10.5 20.5 30.5 40.5

0

2

4

6

8

10

12

Frequency

Body Fat Percentage of Athletes and Obese(%)

-4.5 5.5 15.5 25.5 35.5 45.5

0

2

4

6

8

10

12

Frequency

Body Fat Percentage of Athletes and Obese (%)


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c)

(i) Most of the children have normal and athletes body fat percentage compare to the adults.

The body fat percentange of children in normal categories are 12% to 18% (male) and 19% to

24% (female) while athletes are 5% to 11% (male) and 11%-14% (female).

(ii) Most of the female has overweight body fat percentage compare to male. Female body fatpercentage is 26% to 31%.

b) Ways to help a person to achieve and maintain a healthy life depending on body fatpercentage:

Essential fat category

First of all, fill up on colorful fruits and vegetables. Fruits and vegetables are the foundation

of a healthy diet. Try to eat a rainbow of fruits and vegetables every day and with everymealthe brighter the better. Colorful, deeply colored fruits and vegetables contain higher

concentrations of vitamins, minerals, and antioxidantsand different colors provide different

benefits, so eat a variety. Next , try to limit sugars and salts.. So, some tips that we can

practising it every day is try to avoid sugary drinks. Try sparkling water with lemon or a

splash of fruit juice. We also recommended eating naturally sweet food such as fruits, peppers

or natural peanut butter to satisfy our sweet tooth.

Athletes category

Watch your carbs. Carbohydrates are the chief source of energy in a diet plan for athletes.

Maintain a healthy level of daily calorie intake. Maintain an adequate intake of the right kind

of fats.Proteins are essential to build strength and body weight. Around 10 to 12 % of daily

calorie intake should be lean proteins which may be derived from a varied diet. Include a

range of fruits, veggies, nuts, dairy products, and whole grains in the diet. Eating fruits likebananas, oranges, and potatoes help maintain potassium levels. Stay away from sugary drinks

and sweets as they result in drastic blood glucose level fluctuations which may cause

premature exhaustion and dehydration. Curb the caffeine.

Normal category

Eat fruits and vegetables. Bread, other cereals and potatoes should be taken.This group

includes breakfast cereals, pasta, rice, noodles, oats and other cereals as well as bread and

potatoes. You should aim to include at least one food from this group at each meal. Milk and

dairy foods, 2-3 servings daily is the recommended healthy eating level. Eat meat, fish and

alternatives.This group includes eggs, poultry, and meat and fish products such as beefburgers

and fishcakes. Some of these products can be high in fat - so its best to choose lower fat

versions of products, and trim visible fat from meat and poultry. Alternatives are non-meat

sources of protein such as nuts, tofu, mycoprotein, textured vegetable protein (TVP) and

kidney beans. Eat in small quantities foods containing fat and foods containing sugar.


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Overweight category

You should eat less meat. Select very lean cuts of meat. Trim skin off chicken and turkey.You

should avoid fried meat, chicken, fish, or seafood. You should eat no more than two whole

eggs per week. You should avoid dairy products containing more than 1% milk fat, such as

butter, sour cream, cream cheese, creamed cottage cheese, and most natural and processedcheeses. Select milk products that contain only up to 1% milk fat. Use polyunsaturated

margarine.You must avoid packaged foods or bakery items that contain egg yolks, whole

milk, saturated fats, cream sauces, or butter. Select only those that have a low-cholesterol

rating.You should avoid cashews, coconut, pistachios, and macadamia nuts. Avoid cured or

smoked meat, poultry, or fish. Avoid frozen, canned, and dehydrated main-dish foods such as

pizza, TV dinners, spaghetti, chili, stews, and soups.You should avoid canned vegetables and

vegetable juices, cheese, buttermilk, and cocoa mixes.Most important for you is to avoid

commercial sauces, mayonnaise, salad dressing, olives, pickles, meat tenderizers, and

seasoning salts.

Obese category

Eat 6 to 8 servings of grain products per day (emphasize whole grain), 7 to 10 servings of

vegetables and fruit per day, 2 to 3 servings of low-fat milk products per day and 2 to 3

servings of low-fat meat and alternatives per day.Choose complex carbohydrates more often

and reduce the amount of simple carbohydrates (sugars) you eat. Complex carbohydrates are

found in vegetables, fruits, and whole grains, which are also good sources of vitamins,

minerals, and fibre.Increased fibre intake can help weight loss by reducing absorption of food

and by aiding in digestion. A diet rich in fibre can help by making you feel fuller. Some

experts recommend 20 g to 30 g of fibre daily, with an upper limit of 35 g.Drink more water

and less pop, juice, and specialty coffees or teas, as they contain lots of calories.Replace some

carbohydrate with protein to help you feel full longer.Always eat breakfast.Watch your

portion sizes.

The most important thing is we must exercise regularly in every week. Some warm up and

stretching can release our stress in a right way and also promotes bowel movement. Some

basic exercise that we can do every day is weight-bearing exercise such as walking and

weight training. This exercise can prevent and also slow down bone loss and enchanting theblood flow in the blood capillaries by giving the suitable pressure in the capillaries.


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Reflection

While Im conducting this project, there are many new things that Ive learnt from my

family, teacher, friends and also from the information in internet. One of the things that Ive

learnt is now I know how to create many types of graphs by using Microsoft Excel 2007 such

drawing of histogram and ogive graph. Before this, I never know how use Microsoft Excel

and I dont even want to learn about it but this project had forced me to learn about it in order

to complete this project. At least, Ive learnt something new.

While doing this project, theres plentiful of moral values that I did practice. One of itis patience is the cure of anger. Theres always a mistake when drawing a graph using

Microsoft Excel as Im new with Excel and not use with it. This sometimes wasting my time

without gaining any result. However, its what we called as life and it taught me to be strong

and never give up in completing this project work.


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CONCLUSIONThe conclusion is we can categories a person in five categories. First categories are

essential fat, then athletes, normal, overweight and lastly obese. The categories were

differentiating from the others by a fixed body fat percentage range for each category. A

person is called as essential fat if his body fat percentage is 3-4%, while she is 11-14%. The

athletes will have 5-11% (male) and 15-18% (female). The normal category usually will have

12% to 15% in male category while female is 19% to 24%. An overweight person has body

fat percentage that is 19% to 24% in male and 26% to 31% in female. When a person has a

higher body fat percentage than that range, that person will be called as obese as if his body

fat percentage is higher than 24% and her body fat percentage is 31%.

From the survey that have been done, we can conclude that the majority of the

respondents are in the athletes and normal category. However, there are still respondents who

are in overweight and obese categories. A few of them were in essential fat category. This

shows us that nowadays, people dont like tobe fat.

A healthy person or in the other word the normal person is someone that doesnt doing

something in extreme. People often think of healthy eating as an all or nothing proposition,

but a key foundation for any healthy diet is moderation. Despite what certain fact diets would

have you believe, we all need a balance of carbohydrates, protein, fat, fiber, vitamins, andminerals to sustain a healthy body. So, we should eats moderately and always follow the daily

requirement of the human body. As conclusion, we must take care of our healthy body.


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REFERENCEShttp://en.wikipedia.org/wiki/History_of_statisticshttp://en.wikipedia.org/wiki/Statistics

http://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a49

6.html

http://www.newsmax.com/FastFeatures/diet-tips-for-athletes/2010/11/09/id/371695

http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&

relation_id=107951

Sasbadi Nexus SPM A+ Additional Mathematics refrence book
http://en.wikipedia.org/wiki/History_of_statisticshttp://en.wikipedia.org/wiki/History_of_statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a496.htmlhttp://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a496.htmlhttp://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a496.htmlhttp://www.newsmax.com/FastFeatures/diet-tips-for-athletes/2010/11/09/id/371695http://www.newsmax.com/FastFeatures/diet-tips-for-athletes/2010/11/09/id/371695http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&relation_id=107951http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&relation_id=107951http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&relation_id=107951http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&relation_id=107951http://chealth.canoe.ca/channel_section_details.asp?text_id=4369&channel_id=2053&relation_id=107951http://www.newsmax.com/FastFeatures/diet-tips-for-athletes/2010/11/09/id/371695http://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a496.htmlhttp://www.steadyhealth.com/articles/Best_meal_plan_for_overweight_persons__a496.htmlhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/History_of_statistics

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