95768891 project work additional mathematics 2012 sample answer

PROJECT WORK2012

ADDITIONAL MATHEMATICS

STATISTICS

NAME : NUR SYAFIQAH BT MUHAMMAD FAIZAL SELVARAJ

SCHOOL : SBPI GOPENG

CLASS : 5 RAZI

IC NUMBER : -------------

TEACHERS NAME : MDM.HARNIZAH BT ABDUL RAZAK

PROJECT WORK ADDITIONAL MATHEMATICS 2012

CONTENT

BIL ELEMENT PAGE1 INTRODUCTION 32 APPRECIATION 43 A BRIEF HISTORY OF

STATISTICS 5

4 PART A 75 PART B 116 PART C 137 FURTHER EXPLORATION 198 REFLECTION 229 CONCLUSION 23

2


INTRODUCTIONWe 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 non-routine 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.

APPRECIATION3


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

Mdm. Harnizah Bt. Abdul Razak 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 friends for

helping me collect the much needed data and statistics for this. Not forgetting to all the

others people who were involved directly or indirectly towards making this project a

reality.

I thank you all ..

A BRIEF HISTORY OF STATISTICS

4


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

"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

5


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.

6


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 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.

7


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

8


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.

9


PART B10


A. Line Graph

B. Pie Chart

11

Class Frequency, f0 19 2620 29 3830 39 3240 49 2950 59 1860 69 1670 79 680 89 490 99 1


C. Bar Chart

Modal Class : 20 - 29

Mode : 28

12


Median : 35

Mean : 38.24118

*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

= 90 + 99 - 0 + 19

2 2

= 85

*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:

13


*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.

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

increase based on the comparison.

14

Class Frequency,f Midpoint,x f(x) f(x)0 19 26 4.5 117 526.520 - 29 38 24.5 931 22809.530 39 32 34.5 1104 38088

40 49 29 44.5 1290.5 57427.2550 59 18 54.5 981 53464.5

60 69 16 64.5 1032 6656470 79 6 74.5 447 33301.580 89 4 84.5 338 2856190 - 99 1 94.5 94.5 8930.25

170 480.5 6335 309672.5


PART CX 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 )

15

n X Y XY x y1 1 10 10 1 1002 2 20 40 4 4003 3 30 90 9 9004 4 40 160 16 16005 5 50 250 25 25006 6 60 360 36 36007 7 75 525 49 56258 8 80 640 64 64009 9 85 765 81 722510 10 90 900 100 8100

Total 55 540 3740 385 36450


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 )

( 2 )

16

X Y x y1 1 10 1 1002 2 20 4 4003 3 30 9 9004 4 40 16 16005 5 50 25 25006 6 60 36 36007 7 75 49 56258 8 80 64 64009 9 85 81 722510 10 90 100 8100

Total 55 540 385 36450


17


Prediction of score for student who spent 7 hours per week is 68%.

(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.

18


FURTHER EXPLORATION

x 1.2 2.4 2.8 3.2 3.9 4.3y 9.13 3.23 2.56 1.83 1.56 1.35

0.079 0.380 0.447 0.544 0.591 0.6330.96 0.51 0.41 0.26 0.19 0.13

(1)

19


2 ( i )

20


(ii) Statistically

21


REFLECTIONAdditional Mathematics...

From The Moment I Was Born...From The Moment I Was Able To Hold a Pencil...

From The Moment I Start Learning...And..

From The Moment I Started to Know Your Name...I Always Thought That You Will Be My Greatest Enemy

AndRival In Excelling In My Life...

But After Countless Of Hours...Countless Of Days...

Countless Of Seasons...After Sacrificing My Precious Time Just For You...

Sacrificing My Handphones...Sacrificing My Camera...

Sacrificing My Ipod...Sacrificing My Korean Movies...

Sacrificing My Facebook...I Realized Something Really Important In You...

I Really Love You...You Are My Best Friend Forever...

You Are My Superheroes...You Are My Soul Mate...

I YOU ADDITIONAL MATHEMATICS.22


CONCLUSION

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.

23