2007 F4 Add Math Projects

Obesity is another term for excess body fat. Normal body fat percentages range from 18%-23% in men and 25%-30% in women. Men with body fat percentage greater than 25% and women with a body fat percentage greater than 3% are considered obese. Obesity occurs when intake of calories exceeds the daily caloric requirement. The National Institute of Health (NIH) classifies obesity as a chronic disease, which requires a lifelong effort.

Determining if an individual has excess body fat can be done by various methods. These methods include body density using underwater body weight, dual x-ray absorptiometry (DEXA), measuring skin-fold thickness, computed tomography (CT), and magnetic resonance imaging (MRI). The DEXA test and weighing an individual underwater are most accurate methods, although they can be expensive, time consuming and are not always practical.

The two most common methods for measuring a person’s excess body fat

are

“weight-for-height”

measurement.

The

tables

weight-for-height

and

body

tables

mass

provide

index a

(BMI)

range

of

acceptable weights for a person of a given height. There are many

versions of these tables with different weight ranges, which limit their use. Because of variability of these tables, BMI has become the measurement of choice for many doctors and researchers. BMI is calculated using a mathematical formula that accounts for a person’s height and weight. BMI is equal to a person’s weight in kilograms (kg) divided by height in meters squared (BMI=kg/m²).

For both men and women, normal BMI is between 20 and 24.9. Individuals with a BMI of 25 to 29 are considered to be overweight. Individuals with a BMI of 30 or higher are considered to be obese.

Student

Height(m)

Weight(kg)

1

1.73

43

2

1.77

54

3

1.62

50

4

1.58

45

5

1.65

48

6

1.78

50

7

1.60

50

8

1.63

53

9

1.68

44

10

1.75

85

11

1.69

75

12

1.58

35

13

1.76

57

14

1.74

73

15

1.68

50

16

1.55

44

17

1.62

38

18

1.62

46

19

1.6

49

20

1.69

53

21

1.6

58

22

1.67

43

23

1.69

56

24

1.71

68

25

1.71

56

26

1.75

50

27

1.68

52

28

1.65

54

29

1.55

50

30

1.7

52

31

1.68

70

32

1.63

45

33

1.65

50

34

1.88

75

35

1.72

54

36

1.59

41

37

1.6

47

38

1.52

45

39

1.58

52

40

1.74

62

41

1.75

50

42

1.71

49

43

1.58

45

44

1.67

50

45 46 Weight 35-44 47 45-54 55-64 48 65-74 49 75-84 85-94 50 95-104

Weight of the student in class 3 statistical graphs:

1.7 1.72 1.88 1.72 1.76 1.86

75 Frequency 6 28 6 4 4 1 1

54 75 70 60 104

Histogram

Polygon

Frequency

30 25 20

t n 15 e d u tS

Frequency

10 5 0 35-44

45-54

55-64

65-74

75-84

85-94

95-104

Weight(kg)

Bar Chart

Weight , (kg) 35-44 45-54 55-64 65-74 75-84 85-94 95-104

Frequen cy, ƒ 6 28 6 4 4 1 1

Midpoint, χ 39.5 49.5 59.5 69.5 79.5 89.5 99.5

Midpoint x Frequency, ƒχ 237 1386 357 278 318 89.5 99.5

Means,  = sum of (frequency x class mark) Total frequency = Σƒχ Σƒ

Cumulativ e Frequency 6 34 40 44 48 49 50

Upper Boundary 44.5 54.5 64.5 74.5 84.5 94.5 104.5

= 237+1386+357+278+318+89.5+99.5 6+28+6+4+4+1+1 = 2765 50 = 55.3kg

Median Class = 45-54 Therefore , median, m = L + N/2-F x C fм = 44.5 + 50/2-6 x 10 28 = 44.55 + 6.79 = 51.29kg

From the histogram, mode = 49.5kg Comments on values obtained: Mean

- mean is the best measure of central tendency because all the value in a set of data are taken into consideration while

calculating the mean. Mean is also suitable representing data which are evenly distributed. Median

Mode

- median is used when there are extreme values because median eliminates the effects of extreme values in the set of data. - mode is used to represent a set of data containing a large number of values which take only some specific values and many repeated values.

Therefore,I will choose mean because it is the best measure of central tendency.

Standard deviation Method 1 : Using calculator n



Σχ

Σχ²

50

55.3

27.65

161722

Standard deviation 13.28

Method 2 : Using formula 1 Weight (kg) 35-44 45-54 55-64 65-74

Frequency,ƒ Midpoint , χ 6 39.5 28 49.5 6 59.5 4 69.5

ƒχ 237 1386 357 278

ƒχ² 936105 68607 21241.5 19321

75-84 85-94 95-104

4 1 1 Σƒ = 50

79.5 89.5 99.5

318 89.5 99.5 Σƒχ = 2765

25281 8010.25 9900.25 Σƒχ² = 161722

Mean, = 55.3kg σ ² = Σƒχ² - (Σƒχ)² Σƒ = 161722/50-(2765/50)² = 176.35kg σ = 176.51/2 =13.28kg

Method 3 : Using formula 2

Weight (kg) 35-44 45-54 55-64 65-74 75-84 85-94 95-104

Frequency, ƒ 6 28 6 4 4 1 1 Σƒ = 50

 = 55.3kg σ² = Σƒ( χ -  )²

Midpoint, χ

( χ -  )²

ƒ( χ -  )²

39.5 49.5 59.5 69.5 79.5 89.5 99.5

249.64 33.64 17.64 201.64 585.64 1169.64 1953.64 Σ( χ -  )² = 4211.48

1497.84 941.92 105.84 806.56 2342.56 1169.64 1953.64 Σƒ( χ -  )² = 8818

Σƒ = 8818 50 = 176.36kg σ = 176.361/2 = 13.28kg

D) Conclusion: The value of the standard deviation σ = 13.28kg indicates that there is a wide dispersion from the value of mean obtained. Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Height (m) 1.73 1.77 1.62 1.58 1.65 1.78 1.60 1.63 1.68 1.75 1.69 1.58 1.76 1.74 1.68 1.55 1.62 1.62 1.60 1.69 1.60 1.67

Weight (kg) 43 54 50 45 48 50 50 53 44 85 75 35 57 73 50 44 38 46 49 53 48 43

BMI 14.37 17.24 19.05 18.03 17.63 15.78 19.53 19.95 15.59 27.76 26.26 14.02 18.4 24.11 17.72 18.31 14.48 19.53 19.14 18.56 18.75 15.75

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

1.69 1.71 1.71 1.75 1.68 1.65 1.55 1.70 1.68 1.63 1.64 1.88 1.72 1.59 1.60 1.52 1.58 1.74 1.75 1.71 1.58 1.67 1.70 1.72 1.88 1.72 1.76 1.88

56 68 56 50 52 54 50 52 70 45 50 75 54 41 47 45 52 62 50 49 45 50 75 54 75 70 60 104

19.6 23.26 19.15 16.31 18.42 19.83 20.81 18 24.8 16.93 18.37 21.22 17.84 16.22 18.36 19.48 20.83 20.48 16.33 16.76 18.03 17.93 25.95 18.25 21.22 23.66 19.37 30.06

From the investigate and the report made, the problems of obesity must be persevere since obesity cause not only physical change but also endanger the life of the person. In order to prevent obesity, diet control is very important. Have a balanced diet everyday for enough nutrition and energy especially for those who undergone adolescence. Eat more fruit and vegetables to gain enough vitamins and fibre, taken enough amount protein and carbohydrate from meat and rice and also noodle. Prevent from drinking too much carbonate drink since it contains a lot of sugar that might cause obesity. We also prevent from taking too much junk food since there are no nutrition. Moreover, we must have enough exercise for our body. Exercise twice or three times in a week for a healthy body. Not only sit on the sofa but taking a walk after dinner or lunch to improve digestion of food inside the stomach.

BMI

Frequency

Cumulative frequency

Upper boundary

6-10

0

0

10.5

11-15

3

3

15.5

16-20

34

37

20.5

21-25

9

46

25.5

26-30

3

49

30.5

31-35

1

50

35.5

From the ogive above, it shows that • About 52 % of the student are underweight • About 40% of the student are normal weight •

About 2% of the student are overweight

• Only 2% of the student are obese •

The mean of the BMI = Σƒχ Σƒ = 965.43 50 = 19.3

• Most of the student are not obese but underweight or normal weight.

From the investigation and the report made, the problem of obesity must be dealt with the right measures since obesity can cause not only physical change but also endangers the life of the person. Therefore, everyone must work together to overcome this crucial problem. As student, we must play our respective role too.

In order to prevent obesity, a good diet is very important. Having a daily balanced diet, especially for those who are undergoing adolescence, is a positive step towards a healthy lifestyle. Avoid drinking too much carbonated drinks since they contain lots of sugar that might cause obesity. We should also avoid eating too much junk food since they are not nutritious.

Moreover, we must exercise regularly. Exercising twice or three times a week will lead to a healthy body. We should take a walk after dinner or lunch to improve digestion of the food inside our stomach. Swimming is also a much-recommended exercise for obese people as it takes away much pressure from the feet.

Should the problem persist, we should encourage them to seek proper medical advice from qualified dieticians. These dieticians will be able to recommend the most appropriate and safest diet for each individual to lose weight. After all, doctors know best.

In conclusion, the problem of obesity should not be taken lightly as it can be life-threatening. As student, we should show our full support to help make the “ Obesity Awareness Campaign ” a success.