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YEAR OF EXAMINATION: SUBJECT:

2017

Additional

Mathematics CANDIDATE NUMBER: 0901000361 CANDIDATE NAME:

Ann-Marie L.

Khadoo TITLE OF PROJECT:

To compare

the number of students with

a body

mass index (BMI) of above 41 with a body mass index below 25 in Form 5. TEACHER’S NAME: Nand Prasad

Krishna

1

TABLE OF CONTENT Acknowledgement

3

Introduction

4

Title

5

Purpose of the project

6

Methods of data collection

7

Presentation of Data

8

Analysis of Data

11

Recommendation

12

Conclusion

13

Bibliography

14

Appendix

15

2

ACKNOWLEDGEMENT I would like to express my special thanks and gratitude to my Additional mathematics teacher as well as the principal who gave me the golden opportunity to do this wonderful project on the research topic ‘To compare the number of students with a body mass index (BMI) of above 27 with a body mass index below 25 in form 5.’ Secondly, I would like to thank my parents who helped me a lot in financing this project. I would also like to thank my friends for helping and guiding me through this project.

3

INTRODUCTION Obesity is a serious, chronic disease that can have a negative effect on many systems in the body. Students who are obese can develop many diseases which can be life threatening. By using standard deviation, distinctions can be made to see how many students is over-weight, under-weight and have normal weight. In this project the researcher investigates the body mass index (BMI) of the students of Form 5. By using standard deviation the researcher analyses the BMI of these student.

4

TITLE To compare the number of students with a body mass index (BMI) of above 41 with a body mass index below 25 in Form 5.

5

PURPOSE OF THIS PROJECT The reason for doing this particular topic is because; the researcher would be able to find out who has a BMI of over 25. This would allow the researcher to be able to inform the school to set up a program to advice students so that they would be able to have a normal body mass index. Obesity is a serious, chronic disease that can have a negative effect on many systems in the body. People who are overweight or obese have a much greater risk of developing serious conditions, including: heart disease, type 1 diabetes and bone and joint disease.

6

METHOD OD DATA COLLECTION To obtain the data needed, a scale and a metric ruler will be used. A digital bathroom scale is a type of electronic weighing machine, which is used to measure many readings including body fat, BMI, lean mass, muscle mass, water ratio along with body weight. It measures weight in kilograms (kg). A metric ruler is used to measure the length, height and width of an object or the distance between two points, objects or places. It measures the height of a person in meters square (m 2). Firstly the scale will be placed in the class as well as the metric ruler. Next each student will come out one by one to weigh themselves and measure their height using both the scale and ruler. Each weight and height of each student will be recorded in a suitable table and the body mass index will be calculated using this information recorded. This exercise will last for one hour.

7

PRESENTATION OF DATA BODY MASS INDEX BODY MASS INDEX

FREQU ENCY

BMI MIDPOINT

FREQUENCY* MIDPOINT

DEVIATION

SQUARED DEVIAITON

FREQUENCY* SQUARED DEVIATION

UNDER WEIGHT

15- 18.5

5

16.75

83.75

-21.7

470.6

2352.9

NORMAL WEIGHT

18.6-24.9

15

21.7

325.5

-11.7

136.7

2050.8

OVER WEIGHT

25-45

15

35

525

-11.7

136.7

2050.8

TOTAL

∑f=35

∑f(x)=934.25

∑f(X-XX )2 =6454.6

TABLE SHOWING HOW THE BODY MASS INDEX OF THE STUDENTS WERE ANALYSED The mean, x: x=∑fx ∑f 934.25 35 MEAN= 26.7

Standard Deviation, s: 8

s= ∑fx2 – x2 ∑f

s=

6454.6 35

STANDARD DEVIATION=184.4

GRAPH SHOWING THE FREQUENCY OF THE BODY MASS INDEX OF THE STUDENTS 16 14 12 10 FREQUENCY 8

FREQUENCY

6 4 2 0

15- 18.5

18.5-24.9

25-45

BODY MASS INDEX

9

PIE CHART SHOWING THE PERCENTAGE OF FREQUENCY OF THE BODY MASS INDEX OF THE STUDENTS

14%

15- 18.5 18.5-24.9

43%

25-45 43%

THE MODAL CLASS The modal class (mode class) is the class with the highest frequency. In this research, the highest frequency is 15, which is the frequency for classes 18.5-24.9 and 25-45

PROBABILITY 1. The probability of getting a BMI of over 25 is: The number of students that had a BMI of over 25, n (O) = 15 The total number of students,

n(S) = 35 P (O) = 15 = 3 35 7 10

2. The probability of getting a BMI less than 18.5 is: The number of students that had a BMI less than 18.5,

n (U) = 5

The total number of students,

n(S) = 35 P (U) = 5 = 1 35 7

3. The probability of getting a BMI between 18.6 and 24.9 is: The number of students that had a BMI between 18.6 and 24.9, n (N) = 5 The total number of students,

n(S) = 35 P (N) = 15 = 3 35 7

P (O) +P (U) +P (N) = 3 + 1 + 3 = 7 = 1 7 7 Hence, the sum of the three probabilities is 1 ANALYSIS OF DATA Standard deviation is a measure of the dispersion of a set of data from its mean. If the data points are further from the mean, there is higher deviation within the data set. Standard deviation is calculated as the square root of variance by determining the variation between each data point relative to the mean. It is a simple type of algebraic deviation that increases as the variability of the samples increases and remains in the same sort of unit as the observations from which it is derived. When calculating standard deviation each observation is considered. When analyzing the Body Mass Index of the students, the larger the standard deviation of the BMI, the greater the spread of BMI and vice versa. By using standard deviation, distinctions can be made to see how many students is over-weight, under-weight and have normal weight. 11

Being overweight or obese can have a serious impact on health. Carrying extra fat leads to serious health consequences such as cardiovascular disease (mainly heart disease and stroke), type 2 diabetes, musculoskeletal disorders like osteoarthritis, and some cancers (endometrial, breast and colon). These conditions cause premature death and substantial disability The calculations show that it is common for students to have a Body Mass Index of over 25. It also shows that it common for students to have a Body Mass Index of below 25.

RECOMMENDATION The researcher recommends that students who are overweight should do the following:

Eat more fruit, vegetables, nuts, and whole grains.

Exercise, even moderately, for at least 30 minutes a day.

Cut down your consumption of fatty and sugary foods.

Use vegetable-based oils rather than animal-based fats

12

CONCLUSION In conclusion, it was found that there were some students of form 5who are overweight. It was also found that some of the students were under-weight. Students who are overweight should try and lose some weight before it becomes serious and out of control. The students who are underweight should try and gain some weight but not too much so as to turn overweight.

13

BIBLOGRAPHY Toolsie, R. (2004). MATHEMATICS A complete course with CXC questions Volume 2. Chaguanas: Caribbean Educational Publishers Ltd. Mohan-Ram, V. (1983). Statistics and probability CEDAR Press http://timesofindia.indiatimes.com/life-style/health-fitness/weight-loss/Howto-deal-with-being-overweight/articleshow/50665787.cms https://www.khanacademy.org/math/probability/data-distributionsa1/summarizing-spread-distributions/a/calculating-standard-deviation-stepby-step

14

APPENDIX INFORMATION TABLE

NORMALWEIGHT FORM 5 1 2 3 4 5 6 7 8 9 10 11 12

HEIGHTS IN METERES 1.67 1.78 1.69 1.56 1.64 1.56 1.67 1.61 1.89 1.78 1.65 1.69

HEIGHT SQUAR ED 2.79 3.17 2.86 2.43 2.69 2.43 2.79 2.59 3.57 3.17 2.72 2.86

WEIGHT IN KILOGR AM 54.7 61.4 62.8 58.1 60.5 59.7 55.8 61.4 66.5 51.7 59.2 66.9

BODY MASS INDEX 19.61 19.38 21.99 23.87 22.49 24.53 20.01 23.69 18.62 16.32 21.74 23.42 15

13 14 15

1.64 1.65 1.68

2.69 2.72 2.82

62.4 56.2 71.2

23.20 20.64 25.23

HEIGHTS IN METERES 1.26 1.32 1.25 1.33 1.41 1.39 1.24 1.25 1.31 1.27 1.25 1.35 1.27 1.41 1.32

HEIGHT SQUAR ED 1.59 1.74 1.56 1.77 1.99 1.93 1.54 1.56 1.72 1.61 1.56 1.82 1.61 1.99 1.74

WEIGHT IN KILOGR AM 61.2 62.4 58.1 57.8 59.5 62.5 53.9 64.1 66.8 55.7 68.6 63.6 70.4 65.7 69.3

BODY MASS INDEX 38.55 35.81 37.18 32.68 29.93 32.35 35.05 41.02 38.93 34.53 43.90 34.90 43.65 33.05 39.77

HEIGHTS IN METERES 1.67 1.57 1.68 1.69 1.62

HEIGHT SQUAR ED 2.79 2.46 2.82 2.86 2.62

WEIGHT IN KILOGR AM 45.3 39.9 48.6 51.2 46.8

BODY MASS INDEX 16.24 16.19 17.22 17.93 17.83

OVER WEIG HT FORM 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

UNDE RWEIG HT FORM 5 1 2 3 4 5

16

FORMULAS

STANDARD DEVIATION

MEAN

17

View more...
2017

Additional

Mathematics CANDIDATE NUMBER: 0901000361 CANDIDATE NAME:

Ann-Marie L.

Khadoo TITLE OF PROJECT:

To compare

the number of students with

a body

mass index (BMI) of above 41 with a body mass index below 25 in Form 5. TEACHER’S NAME: Nand Prasad

Krishna

1

TABLE OF CONTENT Acknowledgement

3

Introduction

4

Title

5

Purpose of the project

6

Methods of data collection

7

Presentation of Data

8

Analysis of Data

11

Recommendation

12

Conclusion

13

Bibliography

14

Appendix

15

2

ACKNOWLEDGEMENT I would like to express my special thanks and gratitude to my Additional mathematics teacher as well as the principal who gave me the golden opportunity to do this wonderful project on the research topic ‘To compare the number of students with a body mass index (BMI) of above 27 with a body mass index below 25 in form 5.’ Secondly, I would like to thank my parents who helped me a lot in financing this project. I would also like to thank my friends for helping and guiding me through this project.

3

INTRODUCTION Obesity is a serious, chronic disease that can have a negative effect on many systems in the body. Students who are obese can develop many diseases which can be life threatening. By using standard deviation, distinctions can be made to see how many students is over-weight, under-weight and have normal weight. In this project the researcher investigates the body mass index (BMI) of the students of Form 5. By using standard deviation the researcher analyses the BMI of these student.

4

TITLE To compare the number of students with a body mass index (BMI) of above 41 with a body mass index below 25 in Form 5.

5

PURPOSE OF THIS PROJECT The reason for doing this particular topic is because; the researcher would be able to find out who has a BMI of over 25. This would allow the researcher to be able to inform the school to set up a program to advice students so that they would be able to have a normal body mass index. Obesity is a serious, chronic disease that can have a negative effect on many systems in the body. People who are overweight or obese have a much greater risk of developing serious conditions, including: heart disease, type 1 diabetes and bone and joint disease.

6

METHOD OD DATA COLLECTION To obtain the data needed, a scale and a metric ruler will be used. A digital bathroom scale is a type of electronic weighing machine, which is used to measure many readings including body fat, BMI, lean mass, muscle mass, water ratio along with body weight. It measures weight in kilograms (kg). A metric ruler is used to measure the length, height and width of an object or the distance between two points, objects or places. It measures the height of a person in meters square (m 2). Firstly the scale will be placed in the class as well as the metric ruler. Next each student will come out one by one to weigh themselves and measure their height using both the scale and ruler. Each weight and height of each student will be recorded in a suitable table and the body mass index will be calculated using this information recorded. This exercise will last for one hour.

7

PRESENTATION OF DATA BODY MASS INDEX BODY MASS INDEX

FREQU ENCY

BMI MIDPOINT

FREQUENCY* MIDPOINT

DEVIATION

SQUARED DEVIAITON

FREQUENCY* SQUARED DEVIATION

UNDER WEIGHT

15- 18.5

5

16.75

83.75

-21.7

470.6

2352.9

NORMAL WEIGHT

18.6-24.9

15

21.7

325.5

-11.7

136.7

2050.8

OVER WEIGHT

25-45

15

35

525

-11.7

136.7

2050.8

TOTAL

∑f=35

∑f(x)=934.25

∑f(X-XX )2 =6454.6

TABLE SHOWING HOW THE BODY MASS INDEX OF THE STUDENTS WERE ANALYSED The mean, x: x=∑fx ∑f 934.25 35 MEAN= 26.7

Standard Deviation, s: 8

s= ∑fx2 – x2 ∑f

s=

6454.6 35

STANDARD DEVIATION=184.4

GRAPH SHOWING THE FREQUENCY OF THE BODY MASS INDEX OF THE STUDENTS 16 14 12 10 FREQUENCY 8

FREQUENCY

6 4 2 0

15- 18.5

18.5-24.9

25-45

BODY MASS INDEX

9

PIE CHART SHOWING THE PERCENTAGE OF FREQUENCY OF THE BODY MASS INDEX OF THE STUDENTS

14%

15- 18.5 18.5-24.9

43%

25-45 43%

THE MODAL CLASS The modal class (mode class) is the class with the highest frequency. In this research, the highest frequency is 15, which is the frequency for classes 18.5-24.9 and 25-45

PROBABILITY 1. The probability of getting a BMI of over 25 is: The number of students that had a BMI of over 25, n (O) = 15 The total number of students,

n(S) = 35 P (O) = 15 = 3 35 7 10

2. The probability of getting a BMI less than 18.5 is: The number of students that had a BMI less than 18.5,

n (U) = 5

The total number of students,

n(S) = 35 P (U) = 5 = 1 35 7

3. The probability of getting a BMI between 18.6 and 24.9 is: The number of students that had a BMI between 18.6 and 24.9, n (N) = 5 The total number of students,

n(S) = 35 P (N) = 15 = 3 35 7

P (O) +P (U) +P (N) = 3 + 1 + 3 = 7 = 1 7 7 Hence, the sum of the three probabilities is 1 ANALYSIS OF DATA Standard deviation is a measure of the dispersion of a set of data from its mean. If the data points are further from the mean, there is higher deviation within the data set. Standard deviation is calculated as the square root of variance by determining the variation between each data point relative to the mean. It is a simple type of algebraic deviation that increases as the variability of the samples increases and remains in the same sort of unit as the observations from which it is derived. When calculating standard deviation each observation is considered. When analyzing the Body Mass Index of the students, the larger the standard deviation of the BMI, the greater the spread of BMI and vice versa. By using standard deviation, distinctions can be made to see how many students is over-weight, under-weight and have normal weight. 11

Being overweight or obese can have a serious impact on health. Carrying extra fat leads to serious health consequences such as cardiovascular disease (mainly heart disease and stroke), type 2 diabetes, musculoskeletal disorders like osteoarthritis, and some cancers (endometrial, breast and colon). These conditions cause premature death and substantial disability The calculations show that it is common for students to have a Body Mass Index of over 25. It also shows that it common for students to have a Body Mass Index of below 25.

RECOMMENDATION The researcher recommends that students who are overweight should do the following:

Eat more fruit, vegetables, nuts, and whole grains.

Exercise, even moderately, for at least 30 minutes a day.

Cut down your consumption of fatty and sugary foods.

Use vegetable-based oils rather than animal-based fats

12

CONCLUSION In conclusion, it was found that there were some students of form 5who are overweight. It was also found that some of the students were under-weight. Students who are overweight should try and lose some weight before it becomes serious and out of control. The students who are underweight should try and gain some weight but not too much so as to turn overweight.

13

BIBLOGRAPHY Toolsie, R. (2004). MATHEMATICS A complete course with CXC questions Volume 2. Chaguanas: Caribbean Educational Publishers Ltd. Mohan-Ram, V. (1983). Statistics and probability CEDAR Press http://timesofindia.indiatimes.com/life-style/health-fitness/weight-loss/Howto-deal-with-being-overweight/articleshow/50665787.cms https://www.khanacademy.org/math/probability/data-distributionsa1/summarizing-spread-distributions/a/calculating-standard-deviation-stepby-step

14

APPENDIX INFORMATION TABLE

NORMALWEIGHT FORM 5 1 2 3 4 5 6 7 8 9 10 11 12

HEIGHTS IN METERES 1.67 1.78 1.69 1.56 1.64 1.56 1.67 1.61 1.89 1.78 1.65 1.69

HEIGHT SQUAR ED 2.79 3.17 2.86 2.43 2.69 2.43 2.79 2.59 3.57 3.17 2.72 2.86

WEIGHT IN KILOGR AM 54.7 61.4 62.8 58.1 60.5 59.7 55.8 61.4 66.5 51.7 59.2 66.9

BODY MASS INDEX 19.61 19.38 21.99 23.87 22.49 24.53 20.01 23.69 18.62 16.32 21.74 23.42 15

13 14 15

1.64 1.65 1.68

2.69 2.72 2.82

62.4 56.2 71.2

23.20 20.64 25.23

HEIGHTS IN METERES 1.26 1.32 1.25 1.33 1.41 1.39 1.24 1.25 1.31 1.27 1.25 1.35 1.27 1.41 1.32

HEIGHT SQUAR ED 1.59 1.74 1.56 1.77 1.99 1.93 1.54 1.56 1.72 1.61 1.56 1.82 1.61 1.99 1.74

WEIGHT IN KILOGR AM 61.2 62.4 58.1 57.8 59.5 62.5 53.9 64.1 66.8 55.7 68.6 63.6 70.4 65.7 69.3

BODY MASS INDEX 38.55 35.81 37.18 32.68 29.93 32.35 35.05 41.02 38.93 34.53 43.90 34.90 43.65 33.05 39.77

HEIGHTS IN METERES 1.67 1.57 1.68 1.69 1.62

HEIGHT SQUAR ED 2.79 2.46 2.82 2.86 2.62

WEIGHT IN KILOGR AM 45.3 39.9 48.6 51.2 46.8

BODY MASS INDEX 16.24 16.19 17.22 17.93 17.83

OVER WEIG HT FORM 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

UNDE RWEIG HT FORM 5 1 2 3 4 5

16

FORMULAS

STANDARD DEVIATION

MEAN

17

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