Statistics in Our DailyLife - Syima

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Statistics In Our DailyLife

Project Work For Additional Mathematics 2012

Nama: Nur Hasyimah Binti Hassan

Kelas:5 Rajin

Guru Pembimbing:Pn.Wan Mariana Binti Wan Muda

Sekolah Menengah Kebangsaan Bercham


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Introduction

We students taking Additional Mathematics are required to carry out a project work whileweare 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,but each of us are expected

to submitan individually written report.Upon completion of the Additional Mathematics

Project Work,we ar e to gain valuable experiences and able to:

Applyand adapt a variety of problem solving strategies to solve routine and non-routineproblems;Experienceclassroom environments which are challenging, interesting and meaningfulandhence improve their thinking skills.Experienceclassroom environments where knowledge and skills are applied inmeaningfulways in solving real-life problemsExperienceclassroom environments where expressing ones mathematicalthinking,reasoning and communication are highly encouraged and expected

Experienceclassroom environments that stimulates and enhances effective learning.Acquireeffective mathematical communication through oral and writing,and to usethelanguage of mathematics to express mathematical ideas correctly and preciselyEnhanceacquisition of mathematical knowledge and skills through problem-solvinginways that increase interest and confidencePrepareourselves for the demand of our future undertakings and in workplaceRealisethat mathematics is an important and powerful tool in solving real-life problemsand hence develop positive attitude towards mathematics.Trainourselves not only to be independent learners but also to collaborate, tocooperate,

and to share knowledge in an engaging and healthy environmentUsetechnology especially theICT appropriately and effectivelyTrainourselves to appreciate the intrinsic values of mathematics and to becomemorecreative and innovativeRealizethe importance and thebeauty of mathematics


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History of statistic

By the 18th century, the term "statistics" designated the systematic collection ofdemographic and economic data by states. In the early 19thcentury, 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 "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, statisticsincreasingly used probability theory,whose initial results were found in the17th and 18th

centuries, particularly in the analysis of games of chance (gambling). By 1800, astronomyused 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 the 19thcentury, 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 of inductivelogic 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 decisionscience 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 instatistical practices.Today the use of statistics has broadened far

beyond its origins. Individuals and organizations use statistics to understand dataand make informeddecisions throughout the natural and social sciences,

medicine, business,and other areas.

Statistics is generally regarded not as a subfield of mathematics but rather as a distinct, albeit allied,

field. Many universities maintain separate mathematics and statistics departments.

Statistics is also taught indepartments as diverse as psychology, education, and public

health


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PART AThe 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 collectedfrom 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 makingan 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 Inever 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


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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 studystatistics 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 toknow 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 notmake 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 effectivelyconduct 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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PART B1.Construct a frequency table for the data collected using class intervels of

the same size

Range = 79-1

= 78

Number of class interval = 78

10

= 7.8

= 8

Class frequency

0 9 14

1019 6

2029 6

3039 7

4049 4

5059 6

6069 0

7079 7


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A.Pie chart

B. Line graph

C. Bar chart

Number of student's additional

mathematic TOV marks

0

9

10 19

20 29

30 39

40 49

50 59

60 69

70 79

0

2

4

6

8

10

12

14

16

18

0 9 10

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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Modal class :

Mode :

Median :

Mean :

Range= midpoint of highest class-midpoint of lowest class

0

2

4

6

8

10

12

14

16

0

9

10

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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70+79 _ 0+9

2 2

=70

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= fx2

- (x2)

f

= - ( )2

=

=

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


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

result is increase based on the comparison.

PART C

Class frequency, f midpoint,x f(x) f(x2)

0-9 13 4.5 58.5 263.25

10-19 16 14.5 232 3364

20-29 9 24.5 220.5 5402.25

30-39 7 34.5 241.5 8331.75

40-49 4 44.5 178 7921

50-59 5 54.5 272.5 14851.25

60-69 5 64.5 322.5 20801.25

70-79 8 74.5 596 44402

80-89 3 84.5 253.5 21420.75

90-99 1 94.5 94.5 8930.25

71 495 2469.5 135687.75


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X 1 2 3 4 5 6 7 8 9 10

Y 10 20 30 35 45 50 65 70 85 90

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

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11

marks

number each student spent in doing additional mathematics (h)

n X Y XY X2 Y2


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r = 10(3485)[(55)(500)]

[10(485) (552)][10(31600)(500

2)]

r = 7350

(1825)(66000)

r = 7350

10974.97

r = 0.669706

The range of the correlation coefficient is from -1 to 1. Since our result is 0.669706, we canconclude 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 1 10 10 1 100

2 2 20 40 4 400

3 3 30 90 9 900

4 4 35 140 16 1225

5 5 45 225 25 2025

6 6 50 300 36 2500

7 7 65 455 49 4225

8 8 70 560 64 4900

9 9 85 765 81 7225

10 10 90 900 100 8100

Total 55 500 3485 485 31600


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X= 55 = 5.5 2.10 y50 = 158.08 (x 5.5 )

Y= 500 = 5010 y = 158.08x - 869.44 + 50

b=31600 - 5.5x 50

y =158.08x - 819.44

10

485 - 5.52

10

= 2885 = 158.08

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y xy 2 2

1 1 10 10 1 100

2 2 20 40 4 4003 3 30 90 9 900

4 4 35 140 16 1225

5 5 45 225 25 2025

6 6 50 300 36 2500

7 7 65 455 49 4225

8 8 70 560 64 4900

9 9 85 765 81 7225

10 10 90 900 100 8100Total 55 500 3485 485 31600


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


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(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, Im agreed that least square regression line is suitable in

help me for prediction.


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REFLECTION

Additional Mathematics...

From The Day I Born...From The Day I Was Able To Holding Pencil...

From The Day I Start Learning...

And..

From The Day I Heard Your Name...

I Always Thought That You Will Be My Greatest Obstacle

And

Rival In Excelling In My Life...But After Countless Of Hours...

Countless Of Days...

Countless Of Nights...

After Sacrificing My Precious Time Just For You...

Sacrificing My Computer Games...

Sacrificing My Facebook...

Sacrificing My Internet...

Sacrificing My Anime...

I Realized Something Really Important In You...

I Really Love You...

You Are My Real Friend...

You My Partner...

You Are My Soul Mate...

I LOVE ADD MATH


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APPRECIATIONFirst of all, I would like to say Alhamdulillah, for giving me the strength andhealthto do this project work and finish it on time.

Not forgotten to my parents for providing everything, such as money, to buyanything that are related to this project work, their advise, which is themost needed for this project and facilities such as internet, books, computers and

all that. They also supported me and encouraged me to complete this task so thatI will not procrastinate in doing it.

Then I would like to thank to my teacher,Pn.Wan Mariana Binti Wan Muda forguiding me throughout this project. Even I had some difficulties in doing this task,but she taught me patiently until we knew what to do. She tried and tried to teachme until I understand what Im supposed to do with the project work.

Besides that, my friends who always supporting me. Even this project isindividually but we are cooperated doing this project especially in disscussion andsharing ideas to ensure our task will finish completely.Last but not least, any partywhich involved either directly or indirect incompleting this project work. Thank youeveryone.


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CONTENTSINTRODUCTION

APPRECIATION

A BRIEF HISTORY OFSTATISTICS

PART A

PART B

PART C

FURTHER

EXPLORATION

REFLECTION

CONCLUSION


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CONCLUSION

After doing research, answering questions, drawing graphs and

some problem solving, I saw that the usage of statistics is importantin 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 theidea of statistics.

Statistics in Our DailyLife - Syima

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