92679260 My Addmaths Projects Wanp3l3k

7/28/2019 92679260 My Addmaths Projects Wanp3l3k

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INTRODUCTION

APPRECIATION

A BRIEF HISTORY OFSTATISTICS

PART A

PART B

PART C

FURTHER EXPLORATION

REFLECTION

CONCLUSION


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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 hasprepared 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 non-routine problems

Experience classroom environments which are challenging, interesting andmeaningful and hence improve their thinking skills.

Experience classroom environments where knowledge and skills areapplied 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 enhanceseffective learning.

Acquire effective mathematical communication through oral and writing,and to use the language of mathematics to express mathematical ideas correctl y and

precis ely

Enhance acquisition of mathematical knowledge and skills throughprob lem-solvi ng in ways that increase interes t and co nf iden ce

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, tocooperate, 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.


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First and foremost, I would like to thank my Additional Mathematics teacher 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 ..


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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, thenincluding 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 "computer-

intensive" 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.


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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.


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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 educateddecision 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


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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.


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Class Frequency, f

0 - 19 0

20 - 29 5

30 - 39 29

40 - 49 57

50 - 59 38

60- 69 28

70 - 79 15

80 - 89 10

90 - 99 2

A. Line Graph

B. Pie Chart

05

29

57

38

28

1510

20

10

20

30

40

50

60

0 -

19

20 -

29

30 -

39

40 -

49

50 -

59

60-

69

70 -

79

80 -

89

90 -

99

Number of student's additional

mathematic TOV marks

Number of student's

additional mathematic

TOV marks


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C. Bar Chart

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

0 5

29

5738

28

1510 2



0 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60- 69

70 - 79

05

29

57

38

28

1510

2

0

10

20

30

40

50

60

0 - 19 20 -

29

30 -

39

40 -

49

50 -

59

60-

69

70 -

79

80 -

89

90 -

99



Number of student's

additional mathematic

TOV marks


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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 frequency, f midpoint , x f(x) f(x

0 - 19 0 4.5 0 0

20 - 29 5 24.5 122.5 3001.2530 - 39 29 34.5 1000.5 34517.25

40 - 49 57 44.5 2536.5 112874.25

50 - 59 38 54.5 2071 112869.5

60- 69 28 64.5 1806 116487

70 - 79 15 74.5 1117.5 83253.75

80 - 89 10 84.5 845 71402.5

90 - 99 2 94.5 189 17860.5

184 480.5 9688 552266

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

increase based on the comparison.


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X 1 2 3 4 5 6 7 8 9 10Y 10 20 30 40 50 60 75 80 85 90

(2)

Based on the graph above, it is positive linear correlation which 0 < r < 1.

(3)

n X Y XY 1 1 10 10 1 100

2 2 20 40 4 4003 3 30 90 9 900

4 4 40 160 16 1600

5 5 50 250 25 2500

6 6 60 360 36 3600

7 7 75 525 49 5625

8 8 80 640 64 6400

9 9 85 765 81 7225

10 10 90 900 100 8100

Total 55 540 3740 385 36450

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10

Marks

number each student spent in doing additional mathematics (h)


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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)

x y xy1 1 10 1 10

2 2 20 4 40

3 3 30 9 90

4 4 40 16 1605 5 50 25 250

6 6 60 36 360

7 7 75 49 525

8 8 80 64 640

9 9 85 81 765

10 10 90 100 900

Total 55 540 385 3740

X = = 5.5 y-54=9.33(x-5.5)

Y = = 54 y= 9.33x+2.69

b=

=

= 9.33

(2)


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(3)(i)

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


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(ii)

Regression analysis is widely used forprediction, where its use has substantial overlap with

the field ofmachine 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, Im agreed that least square regression line is suitable in help me for

prediction.
http://en.wikipedia.org/wiki/Predictionhttp://en.wikipedia.org/wiki/Predictionhttp://en.wikipedia.org/wiki/Predictionhttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Machine_learninghttp://en.wikipedia.org/wiki/Prediction


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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

(1)


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Series 1

f(x)=-1.522341*x+1.09; R=0.9998

2 (i) graphically

Series 1

f(x)=-1.522341*x+1.09; R=0.9998

(ii) statistically

y-

intercept

=1.09


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a=

a=-1.5

-0.018 = 1.654+

b=b=0.0213


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Additional Mathematics...

F rom The Day I Born...

F rom The Day I Was Able To Holding Pencil ...

F rom The Day I Start Learn ing...

And..

F rom The Day I H eard Your Name...

I Always Thought That You Wi ll Be My Greatest Obstacle

And

Rival I n Excell ing I n My L if e...

But Af ter Countless Of Hours...

Coun tless Of Days...

Countless Of Nights...

Af ter Sacri fi cing M y Precious Time Just For You...

Sacri f icing My Computer Games...

Sacri fi cing My Video Games...

Sacri fi cing M y Facebook...

Sacr if icing My I nternet...

Sacri fi cing My Anime...

I Realized Something Really Important I n You...

I Reall y Love You...

You Are My Real F ri end...

You My Partner...

You Are My Soul Mate...

I LOVE YOU ADDITIONAL MATHEMATICS.


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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 manymore. Therefore, we should be thankful of the people who contribute in the

idea of statistics.

92679260 My Addmaths Projects Wanp3l3k

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