91691352 My Project Work Add Math 2012

Name : YASMIN FATIN BINTI DEAN Class : 5 BOUGAINVILLEA I/C No: 951130-08-5350 Teacher‘s Name: PUAN NAJIHAH BINTI MUSTAFFA

INTRODUCTION APPRECIATION A BRIEF HISTORY OF STATISTICS PART A PART B PART C FURTHER EXPLORATION REFLECTION CONCLUSION

We students taking Additional Mathematics are required to carry out a project work while we are in Form 5.This year the Curriculum Development Division, Ministry of Education has prepared four tasks for us. We are to choose and complete only ONE task based on our area of interest. This project can be done in groups or individually, and I gladly choose to do this individually. Upon completion of the Additional Mathematics Project Work, we are to gain valuable experiences and able to:             

Apply and adapt a variety of problem solving strategies to solve routine and nonroutine problems Experience classroom environments which are challenging, interesting and meaningful and hence improve their thinking skills. Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real -life problems Experience classroom environments where expressing ones mathematical thinking, reasoning and communication are highly encouraged and expected Experience classroom environments that stimulates 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 ways 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 towards 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 values of mathematics and to become more creative and innovative Realize the importance and the beauty of mathematics.

We are expected to submit the project work within three weeks from the first day the task is being administered to us. Failure to submit the written report will result in us not receiving certificate.

First and foremost, I would like to thank my Additional Mathematics teacher, Mrs. Najihah Binti Mustaffa as she gives us important guidance and commitment during this project work. She has been a very supportive figure throughout the whole project. I also would like to give thanks to all my friends for helping me and always supporting me to help complete this project work. They have done a great job at collecting form 4 end of year result for additional mathematics and sharing information with other people including me. Without them this project would never have had its conclusion. For their strong support, I would like to express my gratitude to my beloved parents. Also for helping me to find the mark to complete this project. They have always been by my side and i hope they will still be there in the future. Last but not least, i would also like to thank all the teacher and my friend for helping me collect the much needed data and statistics for this. Not forgetting too all the other people who were involved directly or indirectly towards making this project a reality. I thank you all ..

By the 18th century, the term "statistics" designated the systematic collection of demographic and economic data by states. In the early 19th century, the meaning of "statistics" broadened, then including the discipline concerned with the collection, summary, and analysis of data. Today statistics is widely employed in government, business, and all the sciences. Electronic computers have expedited statistical computation, and have allowed statisticians to develop "computerintensive" methods. The term "mathematical statistics" designates the mathematical theories of probability and statistical inference, which are used in statistical practice. The relation between statistics and probability theory developed rather late, however. In the 19th century, statistics increasingly used probability theory, whose initial results were found in the17th and 18th centuries, particularly in the analysis of games of chance(gambling). By 1800, astronomy used probability models and statistical theories, particularly the method of least squares, which was invented by Legendre and Gauss Early probability theory and statistics was systematized and extended by Laplace; following Laplace, probability and statistics have been in continual development. In the19th century, social scientists used statistical reasoning and probability models to advance the new sciences of experimental psychology and sociology; physical scientists used statistical reasoning and probability models to advance the new sciences of thermodynamics and statistical mechanics. The development of statistical

reasoning was closely associated with the development of inductive logic and the scientific method

Statistics is not a field of mathematics but an autonomous mathematical science, like computer science or operations research. Unlike mathematics, statistics had its origins in public administration and maintains a special concern with demography and economics. Being concerned with the scientific method and inductive logic, statistical theory has close association with the philosophy of science; with its emphasis on learning from data and making best predictions, statistics has great overlap with the decision science and microeconomics. With its concerns with data, statistics has overlap with information science and computer science.

STATISTICS TODAY During the 20th century, the creation of precise instruments for agricultural research, public health concerns (epidemiology, biostatistics, etc.), industrial quality control, and economic and social purposes(unemployment rate, econometry, etc.) necessitated substantial advances in statistical practices.

Today the used of statistic has broadened far beyond its origin. Individuals and organisations use statistics to understand data and make informed decisions throughout the natural and social sciences, medicines, business, and other area.

Statistics are generally regarded not as the subfield of mathematics but rather as a distinct, allied, field. Many universities maintain separate mathematics and statistic departments. Statistic is also taught in department as diverse as psychology , education and public health.

The first reason is to be able to effectively conduct research. Without the use of statistics it would be very difficult to make decisions based on the data collected from a research project. For example, in the study cited in Chapter One, is the difference in recorded absenteeism between psychiatric and obstetrics nurses large enough to conclude that there is meaningful difference in absenteeism between the two units? There are two possibilities: The first possibility is that the difference between the two groups is a result of chance factors. In reality, the two jobs have approximately the same amount of absenteeism. The second possibility is that there is a real difference between the two units with the psychiatric unit being more nurses missing work. Without statistics we have no way of making an educated decision between the two possibilities. Statistics, however, provides us with a tool to make an educated decision. We will be able to decide which of the two possibilities is more likely to be true. We will base this decision on our knowledge of probability and inferential statistics. A second point about research should be made. It is extremely important for a researcher to know what statistics they want to use before they collect their data. Otherwise data might be collected that is uninterpretable. Unfortunately, when this happens it results in a loss of data, time, and money. Now many a student may by saying to themselves: "But I never plan on doing any research." While you may never plan to be involved in research, it may find its way into your life. Certainly, it you decide to continue your education and work on a masters or doctoral degree, involvement in research will result from that decision. Secondly, more and more work places are conducting internal research or are becoming part of broader research studies. Thus, you may find yourself assigned to one of these studies. Finally, many classes on the undergraduate level may require you to conduct research (for example, a research methods or experimental psychology course). In each of these instances, a knowledge of measurements and statistics will be invaluable. The second reason to study statistics is to be able to read journals. Most technical journals you will read contain some form of statistics. Usually, you will find them in something called the results section. Without an understanding of statistics, the information contained in this section will be meaningless. An understanding of basic statistics will provide you with the fundamental skills necessary to read and evaluate most results sections. The ability to extract meaning from journal articles and the ability to critically evaluate research from a statistical perspective are fundamental skills that will enhance your knowledge and understanding in

related coursework. The third reason is to further develop critical and analytic thinking skills. Most students completing high school and introductory undergraduate coursework have at their disposal a variety of critical thinking and analytic skills. The study of statistics will serve to enhance and further develop these skills. To do well in statistics one must develop and use formal logical thinking abilities that are both high level and creative. The fourth reason to study statistics is to be an informed consumer. Like any other tool, statistics can be used or misused. Yes, it is true that some individuals do actively lie and mislead with statistics. More often, however, well meaning individuals unintentionally report erroneous statistical conclusions. If you know some of the basic statistical concepts, you will be in a better position to evaluate the information you have been given. The fifth reason to have a working knowledge of statistics is to know when you need to hire a statistician. Most of us know enough about our cars to know when to take it into the shop. Usually, we don't attempt the repair ourselves because we don't want to cause any irreparable damage. Also, we try to know enough to be able to carry on an intelligible conversation with the mechanic (or we take someone with us who can) to insure that we don't get a whole new engine (big bucks) when all we need is a new fuel filter (a few bucks). We should be the same way about hiring a statistician. Conducting research is time consuming and expensive. If you are in over your statistical head, it does not make sense to risk an entire project by attempting to compute the data analyses yourself. It is very east to compute incomplete or inappropriate statistical analysis of one's data. As with the mechanic discussed above, it is also important to have enough statistical savvy to be able to discuss your project and the data analyses you want computed with the statistician you hire. In other words, you want to be able to make sure that your statistician is on the right track. To summarize, the five reasons to study statistics are to be able to effectively conduct research, to be able to read and evaluate journal articles, to further develop critical thinking and analytic skills, to act a an informed consumer, and to know when you need to hire outside statistical help.

Class 0 - 19

Frequency, f 0

20 - 29 30 - 39 40 - 49 50 - 59 60- 69 70 - 79 80 - 89 90 - 99

5 29 57 38 28 15 10 2

A. Line Graph

Number of student's additional mathematic TOV marks 60

57

50 40

38

30

29

Number of student's additional mathematic TOV marks

28

20 15

10 0

0

5

10

0 - 20 - 30 - 40 - 50 - 60- 70 - 80 - 90 19 29 39 49 59 69 79 89 99

B. Pie Chart

2

Number of student's additional mathematic TOV marks 0 - 19

20 5

10

15

20 - 29

29

28

30 - 39

57

38

40 - 49 50 - 59 60- 69 70 - 79

C. Bar Chart

Number of student's additional mathematic TOV marks 57

60 50

38

40 29

30

15

20 10

28

0

5

Number of student's additional mathematic TOV marks

10 2

0 0 - 19 20 - 30 - 40 - 50 29 39 49 59

60- 70 - 80 - 90 69 79 89 99

Modal Class = 40 - 49 Mode = 40 Median = 50 Mean = 52.652 *The mean is a more suitable measure of central tendency because it reflects the central value around which the data seems to cluster. The mode is not suitable because the data does not seem to cluster about mode

Range= midpoint of highest class-midpoint of lowest class

When comparing the range of two sets of data, the set with a greater range is said have a greater variation or dispersion. Thus, the range of this overall data have a greater dispersion. ∑

Standard Deviation= √

̃

∑

√ √ =15.14 The standard deviation answer is getting from the square root of a variance which is also a measure of dispersion that has same unit as each value of data.

class 0 - 19 20 - 29 30 - 39

f(x)

f(x2)

0 5 29

midpoint , x 4.5 24.5 34.5

0 122.5 1000.5

0 3001.25 34517.25

40 - 49 50 - 59

57 38

44.5 54.5

2536.5 2071

112874.25 112869.5

60- 69 70 - 79 80 - 89 90 - 99

28 15 10 2 184

64.5 74.5 84.5 94.5 480.5

1806 1117.5 845 189 9688

116487 83253.75 71402.5 17860.5 552266

∑

frequency, f

(b) My TOV mark is higher than all three measure of central tendencies. So, my result is increase based on the comparison.

X Y

1 10

2 20

3 30

4 40

5 50

4

5

6 60

7 75

8 80

9 85

10 90

(2) 100 90 80 70 Marks

60 50 40 30 20 10 0 1

2

3

6

7

8

9

10

number each student spent in doing additional mathematics (h)

Based on the graph above, it is positive linear correlation which 0 < r < 1. (3) n 1 2 3 4 5 6 7 8 9 10 Total

X 1 2 3 4 5 6 7 8 9 10 55

Y 10 20 30 40 50 60 75 80 85 90 540

XY 10 40 90 160 250 360 525 640 765 900 3740

1 4 9 16 25 36 49 64 81 100 385

100 400 900 1600 2500 3600 5625 6400 7225 8100 36450

r

√

=

√

√

=0.992887 The range of the correlation coefficient is from -1 to 1. Since our result is 0.992887, we can conclude that the strength of the linear relationship between x and y is strong. Based on data above, I am agreed if more time is taking to make revision in additional mathematics, more mark will get. B(1)

1 2 3 4 5 6 7 8 9 10 Total

X=

= 5.5

Y=

= 54

b= = (2)

= 9.33

x 1 2 3 4 5 6 7 8 9 10 55

y 10 20 30 40 50 60 75 80 85 90 540

y-54=9.33(x-5.5) y= 9.33x+2.69

1 4 9 16 25 36 49 64 81 100 385

xy 10 40 90 160 250 360 525 640 765 900 3740

(3)(i)

Prediction of score for student who spent 7 hours per week is 66%.

(ii) Regression analysis is widely used for prediction, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. So, I’m agreed that least square regression line is suitable in help me for prediction.

(1)

x

1.2

2.4

2.8

3.5

3.9

4.3

y

9.13

3.23

2.56

1.83

1.56

1.35

0.079

0.380

0.447

0.544

0.591

0.633

0.96

0.51

0.41

0.26

0.19

0.13

y

Series 1 f(x)=-1.522341*x+1.09; R²=0.9998

1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

x 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

2 (i) graphically y

Series 1 f(x)=-1.522341*x+1.09; R²=0.9998

1.3

yintercept =1.09

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

x 0.05

0.1

(ii) statistically

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

a= a=-1.5

-0.018 = 1.654+

b= b=0.0213

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After doing research, answering questions, drawing graphs and some problem solving, I saw that the usage of statistics is important in daily life. It is not just widely used in markets but also in interpreting the condition of the surrounding like the air or the water. Especially in conducting an air -pollution survey. In conclusion, statistics is a daily life necessity. Without it, surveys cannot be conducted, the stock market cannot be interpret and many more. Therefore, we should be thankful of the people who contribute in the idea of statistics.