Additional Mathematics
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PROJECT WORK FOR ADDITIONAL MATHEMATICS
C
Grace be upon Allah, the Almighty with his blessing, my Additional Mathematics project is finally a success. There are several factors that helped me doing this project. I have done this project in a group. My friends Ainatul, Jannah, Hidayah, Aisyah and I, worked together and collaborated to make this project a success. We work together in order to collect all the information about the project. However, we are also glad with our fellow friends for giving information about their weight and height. In addition, we will not be able to do this project without our parent’s help. They sacrificed their times and gave support to ensure our project’s success. Last but not least, I would like to thanks to Puan Kamariah Bt Abu Bakar, my Additional Mathematics teacher. She taught me with dedication and given us meaningful advices during her lessons. She also guided us on on how to make this project successful.
Statistics Statistical modeling and analysis, including the collection and interpretation of data, fromm an essential part of the scientific method in diverse fields, including social, mathematical theory of probability, and covers a wide range of topics, from highly abstract areas to topics directly relevant for applications. Research in statistics covers many issues, some closely tied to theoretical principles of statistical inference, and others more concerned with developing and extending techniques for descriptive and exploratory analysis of data. The theory and practice of designing the efficient collection of data through experiments, surveys, and observational studies constitute important areas of statistics. Since computers play a major and often crucial role in statistical research through the analysis of data, statically computation is major subfield. Statiscal are frequently concerned with modeling complex phenomena, especially by developing and applying appropriate probability models to empirical data, and often these efforts are intimately connected to policy-relevent desion-making in business and government. We seek to train statisticians who will contribute theory, develop innovative and useful statiscal models and methods, and conduct serious applied statiscal scientific investigations. Individual statisticians who will vary in their amphasis, but the field includes all these aspects. Statisticians with advanced training are in substantial demand for position in academics teaching and research, in research laboratories and organizations, in government agencies, and in business. As society, science, and the technology of
datahandling grow in complexity, the need for highly qualified statisticians is expected to grow steadily. The Department of Statistics offers courses of study leading to both the PhD and Master’s degrees. The department encourages applications from students with strong mathematical backgrounds who to concentrate on theoretical statistics, students with training in substantive fields whose primary interest is in applied statistics, and student whose backgrounds and interest lie between these two extremes. In addition to for mal course work and dissertation research, students are encouraged to work closely with faculty and to attend seminars concerning current problems in ampirical research and thereby to gain experience with interdisciplinary statiscal research and consulting. All PhD candidates are expected to engage in some teaching during their period of training.
OBJECTIVE
To understand and use the concept of statistics.
To test the understanding of the students about statistics chapter.
To present creative and important ideas.
To explain the connection between calculation and solution.
To complete the task for final exam and SPM examination.
ADDITIONAL MATHEMATICS PROJECT WORK 2007 FORM 4 Obesity can lead to various health problems such as diabetes, heart diseases and stroke.Your school has decided to carry out an “Obesity Awareness Campaign” with the aim to create awareness among students about obesity related health problem. In this campaign, you are required to obtain the heights and weights of 50 students in Form 4 or Form 5. a) Tabulate your data using the following format.
b) Construct a frequency distribution table for the weights obtained using a suitable class interval i) ii)
Represent your data from the frequency distribution table by using three different statiscal graphs. Find the mean, median and mode for the weights of the 50 students. Which one of the three is the best measure of central tendency to represent the data? Explain your choice.
c) Calculate the standard deviation of the weights by using three different methods. [Note: Include “entering raw data into a calculator” as a method]
d) What conclusion can you draw from the value of the standard deviation obtained in part c?
FURTHER EXPLORARTION The body mass (BMI) gives an indication pf the physical state of a person as being underweight, normal, overweight or obese. BMI can be calculated by using the following formula : BMI =
Weight (kg) Height (m) x Height (m)
The table below shows the BMI and the corresponding physical state of a person : BMI Below 18.5 18.5-24.9 25-29.9 30 and above
CATEGORY Underweight Normal Overweight Obese
a) Calculate the BMI for each student. b) Based on the information given and the data collected, determine the percentage of students that are underweight and the percentage of students that obese by drawing an ogive. c) As a student, describe the role that you can play to make the “Obesity Awareness Campaign” a success.
a) Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Height (m) 1.65 1.63 1.60 1.60 1.60 1.61 1.64 1.63 1.65 1.63 1.64 1.57 1.63 1.63 1.64 1.63 1.62 1.60 1.60 1.60 1.65 1.67 1.67 1.74 1.68 1.62
Weight (kg) 52 50 48 44 44 45 46 52 50 67 66 42 41 50 68 42 44 34 38 30 50 56 54 69 56 50
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1.64 1.68 1.69 1.70 1.62 1.60 1.66 1.60 1.52 1.62 1.70 1.65 1.62 1.68 1.62 1.60 1.65 1.52 1.50 1.69 1.65 1.60 1.59 1.61
56 52 50 65 56 49 52 42 30 49 69 53 55 65 58 40 70 71 72 56 55 60 42 49
b) Based on the data collected from (a) Weight (kg) 30-39 40-49 50-59 60-69 70-79 i)
Frequency 4 15 20 8 3
Example of three statiscal graphs
Histogram
20 18 16 14 12 Number of Students 10 8 6 4 2 0
30-39 40-49 50-59 60-69 70-79
FREQUENCY Weight (kg)
Further Exploration Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Height (m) 1.65 1.63 1.60 1.60 1.60 1.61 1.64 1.63 1.65 1.63 1.64 1.57 1.63 1.63 1.64 1.63 1.62 1.60 1.60 1.60 1.65 1.67 1.67 1.74 1.68 1.62
Weight (kg) 52 50 48 44 44 45 46 52 50 67 66 42 41 50 68 42 44 34 38 30 50 56 54 69 56 50
BMI 19 19 19 17 17 17 17 20 18 25 25 17 15 19 25 16 19 13 15 12 18 21 19 18 18 22
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1.64 1.68 1.69 1.70 1.62 1.60 1.66 1.60 1.52 1.62 1.70 1.65 1.62 1.68 1.62 1.60 1.65 1.52 1.50 1.69 1.65 1.60 1.59 1.61
56 52 50 65 56 49 52 42 30 49 69 53 55 65 58 40 70 71 72 56 55 60 42 49
21 19 23 20 19 21 18 18 22 21 13 19 21 23 22 16 19 31 35 20 20 23 17 19
C
Grace be upon Allah, the Almighty with his blessing, my Additional Mathematics project is finally a success. There are several factors that helped me doing this project. I have done this project in a group. My friends Ainatul, Jannah, Hidayah, Aisyah and I, worked together and collaborated to make this project a success. We work together in order to collect all the information about the project. However, we are also glad with our fellow friends for giving information about their weight and height. In addition, we will not be able to do this project without our parent’s help. They sacrificed their times and gave support to ensure our project’s success. Last but not least, I would like to thanks to Puan Kamariah Bt Abu Bakar, my Additional Mathematics teacher. She taught me with dedication and given us meaningful advices during her lessons. She also guided us on on how to make this project successful.
Statistics Statistical modeling and analysis, including the collection and interpretation of data, fromm an essential part of the scientific method in diverse fields, including social, mathematical theory of probability, and covers a wide range of topics, from highly abstract areas to topics directly relevant for applications. Research in statistics covers many issues, some closely tied to theoretical principles of statistical inference, and others more concerned with developing and extending techniques for descriptive and exploratory analysis of data. The theory and practice of designing the efficient collection of data through experiments, surveys, and observational studies constitute important areas of statistics. Since computers play a major and often crucial role in statistical research through the analysis of data, statically computation is major subfield. Statiscal are frequently concerned with modeling complex phenomena, especially by developing and applying appropriate probability models to empirical data, and often these efforts are intimately connected to policy-relevent desion-making in business and government. We seek to train statisticians who will contribute theory, develop innovative and useful statiscal models and methods, and conduct serious applied statiscal scientific investigations. Individual statisticians who will vary in their amphasis, but the field includes all these aspects. Statisticians with advanced training are in substantial demand for position in academics teaching and research, in research laboratories and organizations, in government agencies, and in business. As society, science, and the technology of
datahandling grow in complexity, the need for highly qualified statisticians is expected to grow steadily. The Department of Statistics offers courses of study leading to both the PhD and Master’s degrees. The department encourages applications from students with strong mathematical backgrounds who to concentrate on theoretical statistics, students with training in substantive fields whose primary interest is in applied statistics, and student whose backgrounds and interest lie between these two extremes. In addition to for mal course work and dissertation research, students are encouraged to work closely with faculty and to attend seminars concerning current problems in ampirical research and thereby to gain experience with interdisciplinary statiscal research and consulting. All PhD candidates are expected to engage in some teaching during their period of training.
OBJECTIVE
To understand and use the concept of statistics.
To test the understanding of the students about statistics chapter.
To present creative and important ideas.
To explain the connection between calculation and solution.
To complete the task for final exam and SPM examination.
ADDITIONAL MATHEMATICS PROJECT WORK 2007 FORM 4 Obesity can lead to various health problems such as diabetes, heart diseases and stroke.Your school has decided to carry out an “Obesity Awareness Campaign” with the aim to create awareness among students about obesity related health problem. In this campaign, you are required to obtain the heights and weights of 50 students in Form 4 or Form 5. a) Tabulate your data using the following format.
b) Construct a frequency distribution table for the weights obtained using a suitable class interval i) ii)
Represent your data from the frequency distribution table by using three different statiscal graphs. Find the mean, median and mode for the weights of the 50 students. Which one of the three is the best measure of central tendency to represent the data? Explain your choice.
c) Calculate the standard deviation of the weights by using three different methods. [Note: Include “entering raw data into a calculator” as a method]
d) What conclusion can you draw from the value of the standard deviation obtained in part c?
FURTHER EXPLORARTION The body mass (BMI) gives an indication pf the physical state of a person as being underweight, normal, overweight or obese. BMI can be calculated by using the following formula : BMI =
Weight (kg) Height (m) x Height (m)
The table below shows the BMI and the corresponding physical state of a person : BMI Below 18.5 18.5-24.9 25-29.9 30 and above
CATEGORY Underweight Normal Overweight Obese
a) Calculate the BMI for each student. b) Based on the information given and the data collected, determine the percentage of students that are underweight and the percentage of students that obese by drawing an ogive. c) As a student, describe the role that you can play to make the “Obesity Awareness Campaign” a success.
a) Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Height (m) 1.65 1.63 1.60 1.60 1.60 1.61 1.64 1.63 1.65 1.63 1.64 1.57 1.63 1.63 1.64 1.63 1.62 1.60 1.60 1.60 1.65 1.67 1.67 1.74 1.68 1.62
Weight (kg) 52 50 48 44 44 45 46 52 50 67 66 42 41 50 68 42 44 34 38 30 50 56 54 69 56 50
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1.64 1.68 1.69 1.70 1.62 1.60 1.66 1.60 1.52 1.62 1.70 1.65 1.62 1.68 1.62 1.60 1.65 1.52 1.50 1.69 1.65 1.60 1.59 1.61
56 52 50 65 56 49 52 42 30 49 69 53 55 65 58 40 70 71 72 56 55 60 42 49
b) Based on the data collected from (a) Weight (kg) 30-39 40-49 50-59 60-69 70-79 i)
Frequency 4 15 20 8 3
Example of three statiscal graphs
Histogram
20 18 16 14 12 Number of Students 10 8 6 4 2 0
30-39 40-49 50-59 60-69 70-79
FREQUENCY Weight (kg)
Further Exploration Student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Height (m) 1.65 1.63 1.60 1.60 1.60 1.61 1.64 1.63 1.65 1.63 1.64 1.57 1.63 1.63 1.64 1.63 1.62 1.60 1.60 1.60 1.65 1.67 1.67 1.74 1.68 1.62
Weight (kg) 52 50 48 44 44 45 46 52 50 67 66 42 41 50 68 42 44 34 38 30 50 56 54 69 56 50
BMI 19 19 19 17 17 17 17 20 18 25 25 17 15 19 25 16 19 13 15 12 18 21 19 18 18 22
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1.64 1.68 1.69 1.70 1.62 1.60 1.66 1.60 1.52 1.62 1.70 1.65 1.62 1.68 1.62 1.60 1.65 1.52 1.50 1.69 1.65 1.60 1.59 1.61
56 52 50 65 56 49 52 42 30 49 69 53 55 65 58 40 70 71 72 56 55 60 42 49
21 19 23 20 19 21 18 18 22 21 13 19 21 23 22 16 19 31 35 20 20 23 17 19
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