Add Maths Part 2

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SMK ST TERESA KUCHING, SARAWAK

ADDITIONAL MATHEMATICS PROJECT WORK

YEAR 2013

THE USES OF STATISTICS IN THE STUDY OF THE IDEAL BODY

FAT PERCENTAGE IN THE HUMAN BODY

NAME : Anne Marian Anak Joseph

FORM : 5 Science 2

I/C NUMBER : 960618-13-5256

TEACHER : Madam Jong Oi Wei


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CONTENTChapters Title Pages

1 Content 22 Appreciation 33 Objective 44 Introduction Part 1 5 6

Introduction Part 11 6 (I)

5 Part 1 a) 7 10b) 11 15

6 Part 2 a) 16b) 16 19

7 Part 320

8 Further Exploration 21 349 Reflection 3510 Conclusion 36


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APPRECIATION

First and foremost, I would like to thank God forthe strength and energy that I had in putting this

project together.

Next, I would like to thank the school in giving us this

opportunity in doing this project in addition providing all

the assistance in making this project a success. Other

than that, I would like to thank my family in all the

support and guidance on completing this project not to

mention the expenses on all the materials used in putting

this project together.

I would also like to express my gratitude to our

beloved teacher Mdm. Jong Oi Wei in completing thisproject. During the process of the project I had some

difficulties and misunderstandings here and there on the

completion of the project but with her guidance I had

manage to come in to conclusion to the project.

Besides, that, I would also like to express my

gratitude to my classmates in helping me to complete thisproject as one of the greats said it.

A fine glass vase goes from treasure to trash, the moment it isbroken. Fortunately, something else happens to you and me. Pick up your

pieces. Then, help me gather mine.

Vera Nazarian
http://www.goodreads.com/author/show/186145.Vera_Nazarianhttp://www.goodreads.com/author/show/186145.Vera_Nazarianhttp://www.goodreads.com/author/show/186145.Vera_Nazarianhttp://www.goodreads.com/author/show/186145.Vera_Nazarian


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OBJECTIVESAll of the students in 5 Science 2 are required to carry out an

Additional Mathematics Project Work during mid-term holiday. Thisproject is done individually. Upon completion of the AdditionalMathematics Project Work, I gain valuable experiences and able to:

Apply and adapt a variety of problem solving strategies to solveroutine and non-routine problems.

Improve my thinking skills. Experience classroom environments where knowledge and skills are

applied in meaningful ways in solving real-life problems.

Experience classroom environments where expressing onesmathematical thinking, reasoning and communication are highlyencouraged and expected.

Experience classroom environments that stimulate and enhanceeffective learning.

Acquire effective mathematical communication through oral andwriting and to use the language of mathematics to expressmathematical ideas correctly and precisely.

Enhance acquisition of mathematical knowledge and skills throughproblem-solving in ways that increase interest and confidence.

Prepare ourselves for the demand of our future undertakings and inworkplace.

Realise that mathematics is an important and powerful tool insolving real-life problems and hence develop positive attitude

towards mathematic. Train ourselves not only to be independent learners but also to

collaborate, to cooperate, and to share the knowledge in anengaging and healthy environment.

Use technology especially the ICT appropriately and effectively. Realise the importance and beauty of mathematics.


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INTRODUCTIONStatistical methods date back at least to the 5th century BC. The

earliest known writing on statistics appears in a 9th-century bookentitled Manuscript on Deciphering Cryptographic Messages, writtenby Al-Kindi. In this book, Al-Kindi provides a detailed description of howto use statistics and frequency analysis to decipher encrypted messages.This was the birth of both statistics and cryptanalysis, according to theSaudi engineer Ibrahim Al-Kadi.

TheNuova Cronica, a 14th-century history of Florence by the

Florentine banker and official Giovanni Villani, includes much statisticalinformation on population, ordinances, commerce, education, andreligious facilities, and has been described as the first introduction ofstatistics as a positive element in history.

Some scholars pinpoint the origin of statistics to 1663, with thepublication of Natural and Political Observations upon the Bills ofMortalityby John Graunt. Early applications of statistical thinkingrevolved around the needs of states to base policy on demographic andeconomic data, hence itsstat-etymology. The scope of the discipline of

statistics broadened in the early 19th century to include the collection andanalysis of data in general. Today, statistics is widely employed ingovernment, business, and natural and social sciences.

Its mathematical foundations were laid in the 17th century with thedevelopment of the probability theory by Blaise Pascal and Pierre deFermat. Probability theory arose from the study of games of chance.The method of least squares was first described by Carl FriedrichGauss around 1794. The use of modern computers has expedited large-scale statistical computation, and has also made possible new methodsthat are impractical to perform manually.

Progress and prosperity have their drawbacks and unhealthy conspicuous

consumption is one of them. The most common of this is over-indulgence in food.

Wealth does make people fatter. In recent studies by the World Health Organization

(WHO), Malaysia was ranked 1st. in South-East Asia (6th. in Asia) for obesity. 60% of

Malaysians aged 18 and above have BMI or body mass index of over 23 - categorizing

them as overweight.

According to Malaysias Health Ministry, 1 in 6 Malaysians are either overweight orobese but the Selangor branch of the Malaysian Diabetes Association cited almost
http://en.wikipedia.org/wiki/Al-Kindihttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/Nuova_Cronicahttp://en.wikipedia.org/wiki/Nuova_Cronicahttp://en.wikipedia.org/wiki/Nuova_Cronicahttp://en.wikipedia.org/wiki/History_of_Florencehttp://en.wikipedia.org/wiki/Giovanni_Villanihttp://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/Probability_theoryhttp://en.wikipedia.org/wiki/Blaise_Pascalhttp://en.wikipedia.org/wiki/Pierre_de_Fermathttp://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/Pierre_de_Fermathttp://en.wikipedia.org/wiki/Blaise_Pascalhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/History_of_statistics#Etymologyhttp://en.wikipedia.org/wiki/John_Graunthttp://en.wikipedia.org/wiki/Giovanni_Villanihttp://en.wikipedia.org/wiki/History_of_Florencehttp://en.wikipedia.org/wiki/Nuova_Cronicahttp://en.wikipedia.org/wiki/Frequency_analysishttp://en.wikipedia.org/wiki/Al-Kindi


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one in two Malaysians are either overweight or obese; and that a recent study showedthat 22% of Malaysians above the age of 30 are diabetic.

The New Straits Times in an article dated 15 Oct. 2012, stated that based on a BMI ofover 25, there were only 5% obese Malaysians in 1996 rising to 14% in 2006 and 15% by

2012. They also reported that almost 50% of adult Malaysians are overweight or obese;with about 20% over the age of 30 afflicted by diabetes up from 14% in 2006; and thatanother 33% above the age of 30 have high blood pressure; with three in fourMalaysians doing little or no exercise.

Apart from over-eating, many other factors cause obesity. Besides having an over-healthy appetite, over-eating can be triggered by emotions and habits too. Cyber-eraconveniences and creature comforts promote inactivity - which in turn promotesobesity. Its evident that sedentary lifestyle does affect a broad spectrum ofMalaysians.

Genetics and hormonal imbalance can also cause obesity. In addition, obesity can becaused by psychological pretexts. Low self-esteem caused by being overweight (in thefirst place), can and often do lead to more eating as a way of seeking comfort. Also,repeated failures with dieting do erode self-esteem further and this in turn aggravatesupon over-eating.

Stress, anxiety, depression and chronic pain can lead to over-eating too. Childhoodphysical and emotional abuse; loss of a parent during childhood; marital and familyproblems have also been known to contribute to comfort over-eating. Certainmedical conditions and medicines such as Cushings syndrome or hypothyroidism; ortaking certain antidepressants or corticosteroids can trigger weight gain.

Alcoholic beverages such as beer and many cocktails contain high calories and wherebeer-belly is indeed a common syndrome. Unlike the US where fast food is cheap(hence preferred by the working poor), fast food eateries are the fair of choice forthose with higher disposable incomes in Asia. Consuming American fast foods can bea hint of ones economic standings but undeservedly, are packed with calories andfats. Considering we should ideally consume 1,800 2,000cals a day, a typical fastfood meal can pack a whopping 1,100cals. A common double cheeseburger is about430cals; a serving of medium fries about 360cals; while a cola is about 280cals.Malaysians habitually snack. A portion of nasi lemak is about 700cals. Add a piece of

chicken and that can be 300cals; and teh-tarik is some 90cals. This common snackworks out to be some 1,100cals.

In consolation, the key for many is to be diet-conscious and to exercise. Whether youjog, swim, cycle outdoors or as in the case of beings-of-today, frequent gyms andutilize home exercise equipment, exercise offers loads of benefits. Discover more thanto simply burn calories. As commonly quipped even your skin glows and you feelas fresh as the morning flower. Essentially, exercise bestows a gamut of healthbenefits besides keeping obesity at bay.


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BackgroundObesity is a medical condition in which excess body fat had accumulated to the extent

that is may have an adverse effect on health, leading to reduced life experiencing or

increased health problems.

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

percentage in the human body. As the president of the Science club, you are required

to collect the data randomly which consists of 80 students (below 20 years old) and 40

adults (over 20-55 years old). It is advisable to use equal number of males and females

for each category.

ConjectureBetween men and women, women have higher body fat percentage. Secondly, between

adults, children and babies, babies have the most body fat percentage followed by

children and adults. As our age increases, there would be physiological changes in

our bodies that make our fat percentage increase especially in women.

PART 1 (a)

DATA FOR 80 RESPONDENTS

Respondents Gender (F/M) Height (m) Weight (kg) Age (years)

1 F 1.62 54 16

2 F 1.60 42 16

3 F 1.43 52 17

4 F 1.60 45 17

5 F 1.50 38 17

6 F 1.50 40 17


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7 F 1.50 54 17

8 F 1.49 45 16

9 F 1.62 60 16

10 F 1.69 42 17

11 F 1.60 65 17

12 F 1.63 50 14

13 F 1.51 50 15

14 F 1.57 55 14

15 F 1.52 50 15

16 F 1.53 50 15

17 F 1.49 31 10

18 F 0.93 16 5

19 F 1.25 30 5

20 F 1.49 38 12

21 M 1.62 65 12

22 M 1.65 65 14

23 M 1.73 55 15

24 M 1.80 63 19

25 M 1.20 60 6

26 M 1.10 20 7

27 M 1.64 68 15


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28 M 1.63 47 12

29 M 1.65 62 13

30 M 1.79 70 19

31 M 1.51 50 13

32 M 1.50 41 12

33 M 1.72 49 15

34 M 1.78 60 15

35 M 1.30 36 9

36 M 1.08 20 6

37 M 1.68 70 19

38 M 1.49 50 10

39 M 1.67 60 19

40 M 1.70 70 19

41 F 1.66 56 53

42 F 1.55 50 50

43 F 1.53 56 35

44 F 1.54 50 37

45 F 1.64 97 42

46 F 1.72 61 52

47 F 1.45 56 48

48 F 1.66 65 45


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49 F 1.69 62 49

50 F 1.63 52 25

51 F 1.68 64 45

52 F 1.65 54 31

53 F 1.64 64 39

54 F 1.65 56 54

55 F 1.68 70 29

56 F 1.70 82 50

57 F 1.68 95 53

58 F 1.57 82 55

59 F 1.70 55 49

60 F 1.72 63 52

61 M 1.81 59 27

62 M 1.84 53 22

63 M 1.70 71 22

64 M 1.80 98 33

65 M 1.78 91 22

66 M 1.75 65 34

67 M 1.72 45 21

68 M 1.70 65 20

69 M 1.75 68 26


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70 M 1.78 60 55

71 M 1.81 83 21

72 M 1.78 85 52

73 M 1.78 72 29

74 M 1.87 90 25

75 M 1.93 106 36

76 M 1.81 65 22

77 M 1.72 119 42

78 M 1.75 105 48

79 M 1.75 81 41

80 M 1.71 110 27

From the survey, we see that there likely more obese children than adults. This may be

due to the nearby convenience of the canteen in schools selling fast foods and junk

foods. It is shown that younger children have more body weight than the young adults

and adults. This may be due to the adequate fat intake for essential growth and

development. Adults needs at least 20% to 35% of their daily calories from fat,

teenagers and children older than 3 requires 25% to 35% and babies and toddlers

need even more fat30% to 40% of daily calories. Thirdly, it is evident that as the age

of females increases, their weight also increases. This may be due to the physiological

changes in her body where fat is needed to protect her potential foetus.

(b)Method 1: By manual calculationI found the value of the mean, mode, median, range, interquartile range, variance and

standard deviation by using a calculator and making use of the mathematical

formulae.


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Calculations:

Mean:

=16 + 20 + 20 + 30 + 31 + 36 + 38 + 38 + 38 + 40 + 40 + 41 + 42 + 42 + 45 + 45 +

45 + 47 + 49 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 52 + 53 + 54 + 54 + 55 + 55 +

55 + 56 + 56 + 56 + 56 + 59 + 60 + 60 + 60 + 60 + 60 + 61 + 62 + 62 + 63 + 63 +

64 + 64 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 68 + 68 + 70 + 70 + 70 + 71 +

74 + 81 + 82 + 82 + 82 + 83 + 85 + 90 + 90 + 91 + 95 + 97 + 98 + 105 + 106 +

119

80

=

= 60.63 kg

Mode:

16, 20, 20, 30, 31, 36, 38, 38, 38, 40, 40, 41, 42, 42, 45, 45, 45, 47, 49, 50,

50, 50, 50, 50, 50, 50, 52, 53, 54, 54, 55, 55, 55, 56, 56, 56, 56, 59, 60, 60,

60, 60, 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 68, 68,

70, 70, 70, 71, 74, 81, 82, 82, 82, 83, 85, 90, 90, 91, 95, 97, 98, 105, 106,

119


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Median:

16, 20, 20, 30, 31, 36, 38, 38, 38, 40, 40, 41, 42, 42, 45, 45, 45, 47, 49, 50,

50, 50, 50, 50, 50, 50, 52, 53, 54, 54, 55, 55, 55, 56, 56, 56, 56, 59, 60, 60,60, 60, 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 68, 68,70, 70, 70, 71, 74, 81, 82, 82, 82, 83, 85, 90, 90, 91, 95, 97, 98, 105, 106,

119

=

= 60 kg

Range:

= 119 kg 16 kg

= 103 kg

16, 20, 20, 30, 31, 36, 38, 38, 38, 40, 40, 41, 42, 42, 45, 45, 45, 47, 49, 50,

50, 50, 50, 50, 50, 50, 52, 53, 54, 54, 55, 55, 55, 56, 56, 56, 56, 59, 60, 60,

60, 60, 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 68, 68,70, 70, 70, 71, 74, 81, 82, 82, 82, 83, 85, 90, 90, 91, 95, 97, 98, 105, 106,

119

Range = Highest value Lowest value


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Interquartile Range

Variance,2 =

16, 20, 20, 30, 31, 36, 38, 38, 38, 40, 40, 41, 42, 42, 45, 45, 45, 47, 49, 50,50, 50, 50, 50, 50, 50, 52, 53, 54, 54, 55, 55, 55, 56, 56, 56, 56, 59, 60, 60,60, 60, 60, 61, 62, 62, 63, 63, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 68, 68,70, 70, 70, 71, 74, 81, 82, 82, 82, 83, 85, 90, 90, 91, 95, 97, 98, 105, 106,

119

Q1 =1(n+1) =

1 (81) = 20

th =

= 50

Q3 =3(n+1) =

3

(81) = 60th =

7

= 69

Interquartile range = Q3 - Q1= 69- 50

= 19 kg


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= 162 + 202 + 202 + 302 + 312 + 362 + 382 + 382 + 382 + 402 + 402 + 412 + 422 + 422 +

452 + 452 + 452 + 472 + 492 + 502 + 502 + 502 + 502 + 502 + 502 + 502 + 522 + 532 + 542

+ 542

+ 552

+ 552

+ 552

+ 562

+ 562

+ 562

+ 562

+ 592

+ 602

+ 602

+ 602

+ 602

+ 602

+612 + 622 + 622 + 632 + 632 + 642 + 642 + 652 + 652 + 652 + 652 + 652 + 652 + 652 + 652

+ 682 + 682 + 702 + 702 + 702 + 712 + 742 + 812 + 822 + 822 + 822 + 832 + 852 + 902 +

902 + 912 + 952 + 972 + 982 + 1052 + 1062 + 1192

80

- (60.63)2

= - (60.63)2

= 388.7 kg

Standard deviation,=

Method 2: By using Microsoft ExcelI found the value of mean, mode, median, range, interquartile range,

variance, and standard deviation by putting in the ungrouped data into

Excel which then automatically groups the data. Then, I calculated the

values by using the auto functions provided.

=

.= 19.72 kg


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Mean : 60.63 kg

Mode : 65

Median :60

Range : = 119 16

= 103 kg

Interquartile range : 19 kg

Variance : 388.7 kg

Standard deviation : 19.72 kg


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Part 2

a) i. Estimated mode = 60 kg

ii. The median is 60 kg whereas the interquartile range is 19 kg.

b) i. The mean, mode and median of grouped data

Mean :

=(1. 3)(3. )(. 3)(7. )(. 1)(11. 3)

=

= 60.25 kg

Mode : 60 kg

CLASS INTERVAL TALLY MIDPOINT, x FREQUENCY, f

1-20 /// 10.5 3

21-40 //// / 30.5 6

41-60 //// //// //// //// ////

//// //// /

50.5 36

61-80 //// //// //// //// // 70.5 22

81-100 //// //// 90.5 10

101-120 /// 110.5 3


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Median :

= 40.5 +

()

20

= 54.27 kg

Class Interval Midpoint,x Frequency, f Cumulative

frequency, CF

( 1-20 ) 10.5 3 3( 21-40 ) 30.5 6 9( 41-60 )

50.5 36 45( 61-80 ) 70.5 22 67(81-100 ) 90.5 10 77(101-120) 110.5 3 80

Where,


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(i) The range, interquartile range, and standard deviation of grouped data.

Range :

From (1 20) = 20

Interquartile range :

=

= 63.17 45.39= 17.78 kg

Q1 =Q3 =

4

4

Q3 - Q1


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Standard deviation, :

= 33.7.31.13.1.33.7 (.)2

= 377.1475

= 377.15 kg

The answers in Part 2 are more accurate than the answers in Part 1.

Class Interval Midpoint,x Frequency, f X2 Fx2

( 1-20 ) 10.5 3 110.25 330.75

( 21-40 ) 30.5 6 930.50 558.30

( 41-60 ) 50.5 36 2550.2591809.00

( 6 -80 ) 70.5 22 4970.25 109345.50

(81-100 ) 90.5 10 8190.25 81902.50

(101-120) 110.5 3 12210.25 36630.75


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Part 3

Based on the answers in Part 1 and Part 2, the measurements of centraltendency for Part 1 are more suitable to represent the weights of therespondents. Measurements of central tendency are widely used tocalculate the quantitative data in a study. Compared to grouped data,ungrouped data can represent the data more accurately as it is specific. Inaddition, we are able to collect the mean, mode, and median for the weightof every respondent. In the comparison of method 1 and method 2 used inPart 1, method 2 is more suitable to be used to collect the data. UsingExcel, we are able to determine the central tendencies of the weight of therespondents more accurately and automatically compared to the manual

way which may provoke hazardous miscalculations.


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FURTHER EXPLORATION

a) Body fat percentage of each respondents.

Responden

ts

Gender

(F/M)

Height

(m)

Weight

(kg)

Age

(years)

BMI BODY FAT

%

1 F 1.62 54 16 20.58 21.27

2 F 1.60 42 16 16.41 14.97

3 F 1.43 52 17 25.43 27.89

4 F 1.60 45 17 17.60 16.07

5 F 1.50 38 17 16.89 15.01

6 F 1.50 40 17 17.78 16.35

()() ()

% of Body Fat for Children (19 years & below) = (1.51BMI) (0.70Age) (3.6Gender**) + 1.4Eg.: (1.5119.2)(0.705)(3.60) +1.4 = 26.89%

% of Body Fat for Adult (20 years & above) = (1.20BMI) (0.23Age) (10.8Gender**) + 5.4Eg.: (1.2022.49)(0.2320)(10.81) + 5.4 = 16.99%

Notes:

**Male = 1

**Female = 0


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7 F 1.50 54 17 24.00 25.74

8 F 1.49 45 16 20.27 20.80

9 F 1.62 60 16 22.86 24.71

10 F 1.69 42 17 14.70 11.70

11 F 1.60 65 17 25.39 27.83

12 F 1.63 50 14 18.81 20.01

13 F 1.51 50 15 21.93 24.01

14 F 1.57 55 14 22.31 25.28

15 F 1.52 50 15 21.64 23.57

16 F 1.53 50 15 21.36 23.15

17 F 1.49 31 10 13.96 15.48

18 F 0.93 16 5 18.49 25.82

19 F 1.25 30 5 19.20 26.89

20 F 1.49 38 12 17.11 18.83

21 M 1.62 65 12 24.76 26.78

22 M 1.65 65 14 23.87 24.04

23 M 1.73 55 15 18.37 15.03

24 M 1.80 63 19 19.44 13.85

25 M 1.20 60 6 41.67 56.52

26 M 1.10 20 7 16.53 17.86

27 M 1.64 68 15 25.28 25.47


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28 M 1.63 47 12 17.69 16.11

29 M 1.65 62 13 22.77 23.08

30 M 1.79 70 19 21.84 17.47

31 M 1.51 50 13 21.93 21.81

32 M 1.50 41 12 18.22 16.91

33 M 1.72 49 15 16.56 12.30

34 M 1.78 60 15 18.93 15.88

35 M 1.30 36 9 21.30 23.66

36 M 1.08 20 6 17.14 19.48

37 M 1.68 70 19 24.80 21.94

38 M 1.49 50 10 22.52 24.80

39 M 1.67 60 19 21.51 16.98

40 M 1.70 70 19 24.22 21.07

41 F 1.66 56 53 20.32 17.59

42 F 1.55 50 50 20.81 18.87

43 F 1.53 56 35 23.92 26.05

44 F 1.54 50 37 21.08 22.18

45 F 1.64 97 42 36.06 39.01

46 F 1.72 61 52 20.62 18.18

47 F 1.45 56 48 26.63 26.31

48 F 1.66 65 45 23.58 23.35


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49 F 1.69 62 49 21.70 20.17

50 F 1.63 52 25 19.57 23.13

51 F 1.68 64 45 22.67 22.25

52 F 1.65 54 31 19.83 22.06

53 F 1.64 64 39 23.79 24.97

54 F 1.65 56 54 20.57 17.66

55 F 1.68 70 29 24.80 28.49

56 F 1.70 82 50 28.37 27.94

57 F 1.68 95 53 33.66 33.60

58 F 1.57 82 55 33.26 32.66

59 F 1.70 55 49 19.03 16.96

60 F 1.72 63 52 21.29 18.988

61 M 1.81 59 27 18.01 10.00

62 M 1.84 53 22 15.65 8.32

63 M 1.70 71 22 24.56 19.01

64 M 1.80 98 33 30.24 23.20

65 M 1.78 91 22 28.72 24.00

66 M 1.75 65 34 21.22 12.24

67 M 1.72 45 21 15.21 8.02

68 M 1.70 65 20 22.49 16.98

69 M 1.75 68 26 22.20 15.26


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70 M 1.78 60 55 18.93 4.66

71 M 1.81 83 21 25.33 20.16

72 M 1.78 85 52 26.82 14.82

73 M 1.78 72 29 22.72 15.20

74 M 1.87 90 25 25.73 19.72

75 M 1.93 106 36 28.45 20.46

76 M 1.81 65 22 19.84 13.35

77 M 1.72 119 42 40.22 33.20

78 M 1.75 105 48 34.28 24.70

79 M 1.75 81 41 26.44 16.90

80 M 1.71 110 27 37.61 33.52


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b) Data Collected through graph

Bar Chart

0

5

10

15

20

25

30

35

40

45

50

Ages below 20 Ages 20-55

No.ofrespondentsineachcategory

Respondents

Essential Fats

Athletes

Normal

Overweight

Obese


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Pie Chart

Male

Essential Fats 2.5%

Athletes 7.5%

Normal 40%

Overweight 30%

Obese 20%

Female

Essential Fats 2.5%

Athletes 25%

Normal 40%

Overweight 25%

Obese7.5%


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Female Children

Essential Fats 5%

Athletes 20%

Normal 50%

Overweight 25%

Obese 0%

Female Adults

Essential Fats 0%

Athletes 30%

Normal 30%

Overweight 25%

Obese 15%


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Male Children

Essential Fat 0%

Atletes 0%

Normal 45%

Overweight 30%

Obese 25%

Male Adults

Essential Fat 5%

Athletes 15%

Normal 35%

Overweight 30%

Obese 15%


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OgiveGRAPH OF WEIGHT, KG AGAINST CUMULATIVE FREQUENCY OF THE

RESPONDENTS.

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60 70 80 90 100 110 120 130

C

umulativeFrequency

Weight, kg

Cumulative frequency


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Histogram


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c)i) When compared to adults, children have a higher body fat percentage.

Adequate fat intake is essential to growth and development. Young kids,

especially, need a certain amount of fat in their diets to help the brain and

nervous system develop correctly. Nowadays, children in schools are

exposed to junk foods in their school canteen. Instant foods are mainly

used because of the less preparation time. Being able to access these

unlimited fatty foods, children are taking more than their minimal fat

intake needed.

ii) When compared to males, females have a higher body fat percentage.

Women have more body fat than menabout five percent more. By

nature, a woman's body is developed to protect her and a potential fetus.

As a result, women have more enzymes for storing fat and fewer enzymesfor burning fat. Additionally, the estrogen women have activates fat

storing enzymes and causes them to multiply. Women experience more

changes in hydration levels than men because of their menstrual cycle,

and this can affect body fat measuring, particularly using the BIA method.

Retaining fluid may also cause weight to fluctuate day-to-day during this

period causing additional variation in the body fat percentage.


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(d)Leading a Healthy Life: Five Steps to Living Long and Staying HealthyStep 1: Give your body the energy it needs.Your body needs some foods to stay strong and healthy. Other

foods, if eaten too often, contribute too many illnesses. Here aresome guidelines:

Eat 6-11 servings a day of breads or grains, like rice, pasta, tortillas,or cereal.

Eat 3-5 servings a day of vegetables, like carrots, cabbage,tomatoes, broccoli, or peas.

Eat 2-4 servings a day of fruits, like apples, peaches, mangos,bananas, or fruit juice.

Eat 2-3 servings a day of meat, fish, beans, eggs or nuts, for protein. Eat 2-3 servings a day of dairy products like yogurt, cheese, or

milk. Cut down on alcohol, fatty foods such as butter, grease, or oil, and

junk food like chips or candy.

Step 2: Stay physically active.Regular physical activity helps people:

live longer and feel better throughout their lives be stronger and more flexible build strong bones and fight osteoporosis prevent depression strengthens your ability to fight off illness maintain a healthy body weightIt is best to get at least one half hour of exercise three times a week,

but any amount of exercise is better than none at all! If you do notwant to go jogging or swimming, try going for a brisk walk with afriend, working vigorously in the yard, or riding your bike to work.

Step 3: A healthy mind is part of a healthy body .When you are in a good state of mind, you make good decisions foryourself about your job, your lifestyle, and your health. Here aresome things you can do to keep your mind healthy:

Reduce stress in your life.


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Make time in your life for things that are fun. Make a list of activitiesyou like and sure you have at least a little time each day for doingsomething you enjoy.

Get enough sleep.

Get help if you feel depressed or anxious for more than severaldays at a time. Talk with a friend or your health care provider forsome help.

Step 4: Keep your mind and body free of harmful drugs and alcohol. Tobacco causes more health problems than any other drug and is

the most addictive, most widely used. Cutting down or stopping the

use of cigarettes, cigars, or chewing tobacco can save your healthand save your money.

Too much alcohol is definitely dangerous, causing liver damage,fetal alcohol syndrome, and accidents. The tricky question is howmuch is too much?

Step 5: Get regular health care. Many people think they only need to see a doctor when they are

sick or injured. The truth is, health care providers are also expertsat preventing illnesses and finding and treating problems beforeyou ever feel sick.

Find a health care provider who works WITH you. Know what diseases you are at risk for and attend regular

screenings for them.

Get yourself and the children in your family immunized against life-threatening illnesses.

http://depts.washington.edu/uwcoe/healthtopics/healthylife.html
http://depts.washington.edu/uwcoe/healthtopics/smoking/index.htmlhttp://depts.washington.edu/uwcoe/healthtopics/smoking/index.htmlhttp://depts.washington.edu/uwcoe/services/index.htmlhttp://depts.washington.edu/uwcoe/healthtopics/healthylife.htmlhttp://depts.washington.edu/uwcoe/healthtopics/healthylife.htmlhttp://depts.washington.edu/uwcoe/healthtopics/healthylife.htmlhttp://depts.washington.edu/uwcoe/services/index.htmlhttp://depts.washington.edu/uwcoe/healthtopics/smoking/index.htmlhttp://depts.washington.edu/uwcoe/healthtopics/smoking/index.html


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Reflection

After by spending countless hours, days and night to finish this project

and also sacrificing our time for chatting and movies in this few weeks,

there are several things that we want to say

I've designed a great experiment

And collected all my data.

I've no idea what it all means

I'll get to that stuff later.

I've forgotten all the stats I learned,

And I never learned that much.

I needed it to pass my comps

But since then I've lost touch.

I'll do another lit review

And find another theory,

But when it's time to analyse,

Everything goes bleary.

So I hired a consultant

To tell me what I'd got

He looked at three years of my life

And answered "Not a lot".

"There is no dissertation here,

There aren't any theses

Basically what you have got

Is a great big pile of faeces!"

"You should have called me years ago

Now get this through your head:

You've hired a physician

But the patient is quite dead".


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CONCLUSION

After doing research, answering the questions, drawing graph, plan a table

and some problem solving, I realise that statistics is important in our daily working life

in collecting, organizing, analysing and interpreting numerical information from data.

It is also widely used in the business segment.

About this Additional Mathematics Project Work, is fun and interesting

because I need to plan the project carefully and systematic because it has something

to do with my future. In fact, further exploration was a fun session because it had

opened my mind about statistics and I have known much more about statistics.

In a nutshell, I can apply all the concept and skills that I had in compiling the

data and in solving the problems in Additional Mathematics. I think that this project

work is very beneficial to all of the students. I would also like to thank the one who

contribute the idea of statistics to help me a lot in our business and daily activities

together in our daily life.

Documents

Add Maths Part 2