add math folio complete

7/31/2019 ADD Math Folio Complete

1/25

ADDITIONALMATHEMATICSPROJECT 2012

TITLE :

NAME :

FORM :

IC NUMBER

TEACHERS NAME


2/25

CONTENTS

NO. TITLE1. Introduction2. Appreciation3. History of Statistics4. Part A5. Part B6. Part C7. Further Exploration8. Reflection9. Conclusion


3/25

INTODUCTION

We students of the 5th form who are taking Additional Mathematics as a subject in SPMare required to complete a project. This project can be either done in groups or individually butmust be handed up individually in a written report. Ive gained a load of experiences while in the

process of completing this project.

Throughout this projects course, Ive been able to adapt to variety of problem and comeout with strategies to solve routine and non-routine problems. Ive also been able to experienceclassroom environments which are challenging, interesting as well as meaningful. Hence, I wasable to improve my problem solving skills. Besides that, I also got to experience environmentswhere expressing ones mathematical thinking, reasoning and communication skills are highlyuseful in life.

Furthermore, I was able to acquire effective mathematical, communicative skills throughthe use the language of mathematics to express mathematical ideas correctly and precisely. I canalso express the acquisition of mathematical knowledge and skills through problem solving thatincreases my interest and confidence in solving mathematical problems. I also have learned howto prepare myself for the demands of our future undertakings in as well as out of our work place.

I also realize that mathematics is a powerful and important tool in solving real-life problems.Hence, I started to develop positive attitude towards mathematics.

Moreover, Ive trained myself not only to be an independent learner but also tocollaborate, cooperate and share the knowledge in an engaging and healthy environment with theuse of technology. Finally, I get to train myself to appreciate intrinsic values of mathematics andto become more creative and innovative. While carrying out this project, I realize all theimportance and the beauty of mathematics.


4/25

APPRECIATION

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

Hamisah 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 thanks to all my friends for helping me and to complete this projectwork. They have done a great job at collecting Form 4 end of year result for AdditionalMathematics and sharing information with other people including me. Without them this projectwould never have done.

For their strong support, I would like to express my gratitude to my beloved parents.

They also helping me to find the mark to complete this project. They have always been by myside 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 mecollect the needed data and statistics for this. Not forgetting too all the other people who wereinvolved directly or indirectly towards making this project.


5/25

HISTORY OF STATISTICS

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, 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 allowedstatisticians to develop "computer-intensive" methods. The term "mathematical statistics"designates the mathematical theories of probability and statistical inference, which are used instatistical 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, astronomers used probability models and statistical theories, particularly themethod of least squares, which was invented by Legendre and Gauss. Early probability theoryand statistics was systematized and extended by Laplace. Following Laplace, probability andstatistics have been in continual development. In the19th century, social scientists used statisticalreasoning and probability models to advance the new sciences of experimental psychology andsociology. Physical scientists used statistical reasoning and probability models to advance thenew sciences of thermodynamics and statistical mechanics. The development of statistical

reasoning was closely associated with the development of inductive logic and the scientificmethod.

Statistics is not a field of mathematics but an autonomous mathematical science, likecomputer science or operations research. Unlike mathematics, statistics had its origins in publicadministration and maintains a special concern with demography and economics. Beingconcerned with the scientific method and inductive logic, statistical theory has close associationwith 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.


6/25

STATISTICS TODAY

During the 20th century, the creation of precise instruments for agricultural research,

public health concerns, industrial quality control, economic and social purposes are necessitatedsubstantial advances in statistical practices.

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

Statistics are generally regarded not as the subfield of mathematics but rather as adistinct, allied and field. Many universities maintain separate mathematics and statisticdepartments. Statistic is also taught in department as diverse as psychology, education and publichealth.


7/25

PART A

Research required statistics to be efficient and precise. Without the use of statistics itwould be very difficult to make decisions based on the hard facts that has been collectedthroughout an experiment or finding. For example, in the study area of Chapter One, thedifference is recorded absenteeism between psychiatric and obstetrics nurses large enough toconclude 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. Thesecond 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. However, statistics 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 thisdecision 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 the data

collected might be misinterpret. Unfortunately, when this happens it results in a loss of data, timeand money. Now many student may say to themselves, But I never plan to do any research.While you may never plan to be involved in research, it may find its way into your life. Certainlyyou decide to continue your education and work on a masters or doctoral degree. Involvement inresearch will result from that decision.

Secondly, more and more work places are conducting internal research or becoming a 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. In each of these instances, knowledge of measurements and statistics will be invaluable. The second reasonto study statistics is to be able to read journals. Most technical journals you read contain someform of statistics. Usually, you will find them in something called the results section. Without anunderstanding of statistics, the information contained in this section will be meaningless. Anunderstanding of basic statistics will provide you with the fundamental skills necessary to readand evaluate most results sections. The ability to extract meaning from journal articles and the


8/25

ability to critically evaluate research from a statistical perspective are fundamental skills that willenhance your knowledge and understanding in related coursework.

The third reason is to further develop critical and analytic thinking skills. The study of statistics will serve to enhance and further develop these skills. To do well in statistics one mustdevelop 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 misleadwith statistics. However, more often one individual unintentionally report erroneous statisticalconclusions. If you know some of the basic statistical concepts, you will be in a better position toevaluate the information you have been given.

The fifth reason to have a working knowledge of statistics is to know when you need tohire a statistician. Most of us know enough about cars when to take it to the shop. Usually, wedon't attempt the repair ourselves because we don't want to cause any irreparable damage. We tryto know enough to be able to carry on an intelligible conversation with the mechanic to insurethat we don't get a whole new engine when all we need is a new fuel filter.

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 computeincomplete or inappropriate statistical analysis of one's data. As with the mechanic discussedabove, it is also important to have enough statistical savvy to be able to discuss your project andthe 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 conductresearch to be able to read and evaluate journal articles, to further develop critical thinking andanalytic skills, to act an informed consumer and to know when you need to hire statistical help.


9/25

Data can represented in many ways. Some of them can be represented in the following ways .

Bar Chart

Easy to compare the quantities.

Two sets of data can represent in one chart and the information can be easily read.


10/25

Pie Chart

Easy to compare to each categories.

Easily to read when using computer graphics.


11/25

PART B

Marks Frequency,f

0-9 4

10-19 5

20-29 6

30-39 9

40-49 6

50-59 1

60-69 770-79 6

80-89 7

90-99 4

TOTAL 55


12/25

BAR CHART


13/25

PIE CHART


14/25

LINE GRAPH


15/25

Based on the bar chart, we can measures of central tendencies such as mode, median and mean.

MODE

Mode = Highest frequency

= 30-39 marks (Modal class)

MEDIAN

Median = L + - F C

= 39.5 + - 24 10

6

= 45.333

MEAN

Marks Midpoint, x Frequency , f

fx

0-9 4.5 4 20.25 81 1810-19 14.5 5 210.25 1051.25 72.520-29 24.5 6 600.25 3601.5 14730-39 34.5 9 1190.25 10712.25 310.540-49 44.5 6 1980.25 11881.5 26750-59 54.5 1 2970.25 2970.25 54.560-69 64.5 7 4160.25 29121.75 451.570-79 74.5 6 5550.25 33301.5 44780-89 84.5 7 7140.25 49981.75 591.590-99 94.5 4 8930.25 35721 378

TOTAL 495 55 32752.5 178423.75

2737.5


16/25

Mean =

=

= 49.7727

*The mean is a more suitable measure of central tendency because it reflects the central valuearound which the data seems to cluster. The mode is not suitable because the data does not seemto cluster about mode.

RANGE (Midpoint of highest class Midpoint of lowest class)

Range = -

= 94.5 4.5

= 90

When comparing the range of two sets of data, the set with a greater range is said to have a

greater variation of dispersion. Thus, the range of this overall data have greater dispersion.

Standard deviation


17/25

27.69014

The standard deviation answer is obtained from the square root of a variance which is also ameasure of dispersion that has same unit as each value of data.

b) My TOV marks is higher than all 3 measures of central tendencies, so my result hadincreased based on my comparison.


18/25

PART C

Information and data about the number of hours spend in doing Additional Mathematics per week to the respective TOV marks is obtained by interviewing 10 students in Form 5

STUDENTS 1 2 3 4 5 6 7 8 9 10HOURS ( x ) 9 2 8 6 3 4 4 7 5 9TOV MARKS ( y) 91 14 86 64 32 46 44 75 60 89

A graph is plotted using TOV marks ( y) against the number of hours per week spend in doingAdditional Mathematics ( x). Based on the graph above it is positive linear correlation which 0 < r

< 1

The Pearson correlation coefficient for the data is calculated using the formula

r =

where


19/25

DATA TO CALCULATE THE PEARSON CORRELATION COEFFICIENT

X y xy9 91 819 81 82812 14 28 4 196

8 86 688 64 73966 64 384 36 40963 32 96 9 10244 46 184 16 21164 44 176 16 19367 75 525 49 56255 60 300 25 36009 89 801 81 7921

CALCULATION

i)

57.53

ii)

5.61


20/25

iii)

1207.09

34.74

r

r

r

The Pearson correlation coefficient measures the strength of the linear relationship that exists between x and y either strong or week. The graph shows a strong positive linear correlation

whereby 0 < r < 1. The TOV marks are directly proportional to the number of hours spend indoing Additional Mathematics exercises per week. if more time taken to revise AdditionalMathematics the more marks the student will obtained.

Equation of the least squares regression line, where

y = mx + c

m =

=

= 10.25


21/25

From the graph, c = y - intercept

c = 0

y = 10.25 x

A least square line passes through the point ( ), where = and =

= =

= =

= 5.7 = 60.1

The least square line that passes through is ( ) = (5.7, 60.1)

Draw the least squares regression line on the same axes as the points plotted in graph in Part C

From the least squares regression line from the graph, the score for Additional Mathematics of a

student who spend 7 hours per week in doing Additional Mathematics exercises is 75 marks.

3ii) Regression analysis is at used to understand which among the independent variables arerelated to the dependent among the independent variables are related to the dependent variable. Iagree that the least squares regression line is suitable in helping me in finding the prediction.


22/25

FURTHER EXPLORATION

The value of the constants a and b can be determined graphically and statistically. The

relationship between x and y can be obtained graphically by taking and

x y1.20 0.08 9.13 0.962.40 0.38 3.23 0.512.80 0.45 2.56 0.413.50 0.54 1.83 0.263.90 0.59 1.56 0.194.30 0.63 1.35 0.13

It is graphically shown that the equation correctly describe the relationship between x and y.

y is inversely proportional to x ( y ),that is when x increases y decreases.

y


23/25

GRAPHICALLY:

Gradient = - a

-a = b

-a = b

a = -1.5

STATISTICALLY :

-a =

a = -1.5

When x = 0.079

y = 0.96

-0.018 = 1.654 +

b =

b = 0.0213


24/25

REFLECTION

Additional Mathematics,Are u as easy as a click,

Do u become easier as we speak,You are the one i seek,

you are the one i need.

Since i ever heard of u,i become afraid of ubut when i know u,

u attract me out of the blue.

with u, although it hard to be right,i try my best not to be out of sight,and practices at night

and it is so bright...


25/25

CONCLUSION

After doing research, answering questions, drawing graphs and some problem solving, Isaw that the usage of statistics is important in daily life. It is not just widely used in markets butalso in interpreting the condition of the surrounding like the air or the water. Especially inconducting 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, weshould be thankful of the people who contribute in the idea of statistics.

add math folio complete

Documents