project work add math 2013 pahang

7/23/2019 Project Work Add Math 2013 Pahang

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SEKOLAH BERASRAMA PENUH INTEGRASI TUN ABDUL RAZAK

PULAU SERAI, 26600 PEKAN PAHANG

ADDITIONAL MATHEMATICS PROJECT WORK

2/2013

Index Number in Our Daily Life

NAME

MUHAMAD NAJMIL HAQIM BIN MUSTAFAR

I/C No.

960111 - 06 5543

CLASS5 ABU QATADAH

TEACHER

EN. NOR AZIZI FAIN


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CONTENT

CONTENTS PAGES

OBJECTIVE 2

FOREWARD 3

INTRODUCTION 4 - 5

PART 1 6 - 12

PART 2 13 - 16

PART 3 17 - 18

FUTHER EXPLORATION 19 - 25

REFLECTION 26


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OBJECTIVESWe 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, but each of us are expected to

submit an individually written report. 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 meaningfuland hence improve their thinking skills.

Experience classroom environments where knowledge and skills are applied inmeaningful ways in solving real-life problems

Experience classroom environments where expressing ones mathematicalthinking,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 inways that increase interest and confidence

Prepare ourselves for the demand of our future undertakings and in workplace Realise 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


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FOREWARDFirst of all, I would like to say Alhamdulillah, for giving me the strength and health to do this

project work. Not forgotten my parents for providing everything, such as money, to buy anything

that are related to this project work and their advice, which is the most needed for this project.

Internet, books, computers, and etc. They also supported me and encouraged me to complete

this task so that I will not procrastinate in doing it. Then I would like to thank my teacher, En. Nor

Azizi Bin Fain for guiding me and my friends throughout this project. We had some difficulties in

doing this task, but she taught us patiently until we knew what to do. She tried and tried to teach

us until we understand what we supposed to do with the project work. Last but not least, my

friends who were doing this project with me and sharing our ideas. They were helpful that when

we combined and discussed together, we had this task done.


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INTRODUCTION

HISTORY OF INDEX NUMBER

Index numbers are meant to study the change in the effects of such factors which cannot be

measured directly. According to Bowley, Index numbers are used to measure the changes in some

quantity which we cannot observe directly. For example, changes in business activity in a country

are not capable of direct measurement but it is possible to study relative changes in business

activity by studying the variations in the values of some such factors which affect business activity,

and which are capable of direct measurement.

Index numbers are commonly used statistical device for measuring the combined

fluctuations in a group related variables. If we wish to compare the price level of consumer items

today with that prevalent ten years ago, we are not interested in comparing the prices of only one

item, but in comparing some sort of average price levels. We may wish to compare the present

agricultural production or industrial production with that at the time of independence. Here again,

we have to consider all items of production and each item may have undergone a different

fractional increase (or even a decrease). How do we obtain a composite measure? This composite

measure is provided by index numbers which may be defined as a device for combining the

variations that have come in group of related variables over a period of time, with a view to obtain

a figure that represents the net result of the change in the constitute variables.


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Index numbers may be classified in terms of the variables that they are intended to

measure. In business, different groups of variables in the measurement of which index number

techniques are commonly used are (i) price, (ii) quantity, (iii) value and (iv) business activity.

Thus, we have index of wholesale prices, index of consumer prices, index of industrial output,

index of value of exports and index of business activity, etc. Here we shall be mainly interested

in index numbers of prices showing changes with respect to time, although methods described

can be applied to other cases. In general, the present level of prices is compared with the level

of prices in the past. Thepresent period is called the current period and some period in the past

is called the base period.

Index Numbers:

Index numbers are statistical measures designed to show changes in a variable or group

of related variables with respect to time, geographic location or other characteristics such as

income, profession, etc. A collection of index numbers for different years, locations, etc., is

sometimes called an index series.

Simple Index Number:

A simple index number is a number that measures a relative change in a single variable

with respect to a base.

Composite Index Number:

A composite index number is a number that measures an average relative changes in a

group of relative variables with respect to a base.


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PART 1The price of goods sold in shop vary from one shop to another. Shoppers tend to buy goods

which are not only reasonably price but also give value for their money.

You are required to carry out a survey on four different items based on the following

categories: food, detergent and stationery. The survey should be done in three different shop.

Part 1(a)

Collect picture, newspaper cuttings or photos on item that you have chosen. Design a collage to

illustrate the chosen item.

FOOD


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DETERGENT


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STATIONERY


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Part 1(b)

Record the item and their prices systematically as such in Table 1. Since item may be

differently packed, be sure to use consistent measurements for each item selected so that

comparison can be done easily and accurately.

The data in the table below is only serve as a REFERENCE to you:

Category Item Tesco Giant The Store

Food Self-rising flour 2.70 3.70 3.30

Sugar 1.80 1.60 1.35

Butter 3.60 3.80 4.50

Eggs 3.60 2.90 3.00

Total Price 11.70 12.00 12.15

Detergent Washing Powder 19.00 21.00 20.50

Dish Washer 4.00 3.20 3.10

Liquid Bleach 6.00 5.50 4.90

Tile Cleaner 10.20 9.80 9.50

Total Price 39.20 39.50 38.00

Stationery Pencil (Shaker) 8.90 9.20 8.20

Highlighter 3.50 3.40 3.10

Permanent Marker 3.50 2.90 3.80

Card Indexing 14.70 15.00 16.00

Grand Total 81.50 82.00 82.15


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Part 1(c)

Create at least two suitable graphical representations (the use of ICT is encouraged) to compare

contrast the price of the item chosen.

0

5

10

15

20

25

30

35

40

45

Food Detergent Stationery

Tesco

Giant

The Store

0

5

10

15

20

25

30

35

40

45


Tesco

Giant

The Store


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Part 1 (d):

Based on the graphical representations that you have constructed in part 1(c), interpret,discuss and draw consclusion. Comment on your findings.

Based on the graphical representations that I have constructed in Part 1(c), it is shown

that there are large and small differences among the prices of items in each category between

the shops. In the food category, the smallest price difference are of those of sugar, while the

highest is the price of eggs. Besides food, detergent also shows a large price difference between

its items. Among them is the price of liquid dishwasher and clothes detergent. On the other hand,

stationery items doesnt have any obvious price difference. The graph also show that most of the

items that are high priced comes from the Boulevard Supermarket, while the lowest price items

come from the Discount Store. The graph 1(d) will show the conclusion of the difference among

the shops based upon the shops grand total.

Graph 1(d)0

5

10

15

20

25

30

35

40

45


Tesco

Giant

The Store


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Part 1(e)

The item that has a large price difference = washing powder

Mean , X = =

19+21+20.53 =

1216 = 20.20 (2dp)

Standard deviation = ()2= 1921+20.53 (1216 )2=1222.253 (1216 )2= 0.8498

Reason of difference in price :

Bulk buying from the retailer gives the lower cost resulted in lower relling price. Hypermarket own brands are much cheaper than the expansive brand-dont involve in

advertiving resulted in lower selling price

Sales and discount offer by the supermarket.


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PART 2Every year SBP Integrasi Tun Abdul Razak organises a carnival to raise funds for the school. This

year the school plans to install CCTV in order to enchance its security. Last year, during the

carnival, your class made and sold nasi lemak. Due to the popularity of this local food, your

class has decided to carry out the same project for this ye ars carnival.

Part 2(a)

I.Complete Table 2 with the prices of the given items for the year 2013


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Part 2(b)

Calculate the price index for each of the items in Table 2 for the year 2013 based on the year

2012.


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Part 2(c)

Calculate the composite index for the cost of a packet of nasi lemak in the year2013 based on

the year 2012. Discuss how you obtained your answer.


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Part 2(d)

In the year 2012, the nasi lemakwas sold at RM2.00 each. Suggest a suitable selling price for a

packet of the nasi lemak in the year 2013. Give reasons for your answer.


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PART 3In order to upgrade the security, my school has decided to install closed-circuit TV (CCTV).

Part 3(a)

Suggest a suitable number of cameras to be installed and their placement. Give your reasons.

Illustrate with a plan.

I suggest 4 cameras to be installed at my school. The cameras will be installed at the staff rooms

and the office. This action will be done to avoid any robbery case from happen.

Part 3(b)

Find out the cost of installation of the CCTV.

A set of CCTV with 4 cameras : RM2100


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Part 3(c)

If your class intends to sponsor 10% of the cost, how many packets of nasi lemak must yourclass sell?

10% X RM2100 = RM210

Cost for a packet of nasi lemak =RM13.22

10 = RM1.40

Selling price = RM2.10

Profit = RM2.10 RM1.40

= RM0.70

Packets of nasi lemak must be sell =RM210RM0.70

= 300 packets

Part 3(d)

Can your class achieve the 10% target? Do you think your class should carry out a different

project instead?

Yes because many visitors from Pekan will come and visit our school during the

carnival.This phenomenon will increase the selling of our nasi lemak. Last year, we had sold

about 400 packets of nasi lemak. So, this year our target is 600 packets of nasi lemak will

besold. From the selling, we can sponsor 10% for the cost of installation of the CCTV andwe will

get profit of about RM210. I think my class should not carry out different projectas we can get alot of profit from the selling of nasi lemak. We need to focus on sellingnasi lemak only so we

can achieve our target. Great efforts will led to great outcomes


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FUTHER EXPLORATION

Index numbers are being used in many different daily situations, for example air pollution

index, stock market index, gold index and property index.

Obtain information from the internet or other reliable sources on the importance of two

different types of index number of your choice. Elaborate the use and the importance of these

index numbers in daily life.

Air Pollution Index

Air pollution is the introduction ofchemicals, particulate matter, or biological

materials that cause harm or discomfort to humans or other living organisms, or damages

the natural environment into the atmosphere.

The atmosphere is a complex dynamic natural gaseous system that is essential to

support life on planet Earth. Stratospheric ozone depletion due to air pollution has long been

recognized as a threat to human health as well as to the Earth's ecosystems.

The Air Quality Index (AQI) (also known as the Air Pollution Index (API) or Pollutant

Standard Index (PSI) is a number used by government agencies to characterize the quality of

the air at a given location. As the AQI increases, an increasingly large percentage of the

population is l ikely to experience increasingly severe adverse health effects. To compute the

AQI requires an air pollutant concentration from a monitor or model. The function used to

convert from air pollutant concentration to AQI varies by pollutant, and is different in different

countries. Air quality index values are divided into ranges, and each range is ass igned a

descriptor and a color code. Standardized public health advisories are associated with each AQI

range. An agency might also encourage members of the public to take public transportation or

work from home when AQI levels are high.
http://en.wikipedia.org/wiki/Chemicalhttp://en.wikipedia.org/wiki/Particulate_matterhttp://en.wikipedia.org/wiki/Biological_materialhttp://en.wikipedia.org/wiki/Biological_materialhttp://en.wikipedia.org/wiki/Natural_environmenthttp://en.wikipedia.org/wiki/Earth%27s_atmospherehttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Stratospherehttp://en.wikipedia.org/wiki/Ozone_depletionhttp://en.wikipedia.org/wiki/Ecosystemshttp://en.wikipedia.org/wiki/Ecosystemshttp://en.wikipedia.org/wiki/Ozone_depletionhttp://en.wikipedia.org/wiki/Stratospherehttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earth%27s_atmospherehttp://en.wikipedia.org/wiki/Natural_environmenthttp://en.wikipedia.org/wiki/Biological_materialhttp://en.wikipedia.org/wiki/Biological_materialhttp://en.wikipedia.org/wiki/Particulate_matterhttp://en.wikipedia.org/wiki/Chemical


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Limitations of the AQI

Most air contaminants do not have an associated AQI. Many countries monitor ground-

level ozone, particulates, sulphur dioxide, carbon monoxide and nitrogen dioxide and calculate

air quality indices for these pollutants.

Causes of Poor Air Quality

The AQI can worsen (go up) due to lack of dilution of air emissions by fresh air. Stagnant air,

often caused by an anticyclone or temperature inversion, or other lack ofwinds lets air

pollution remain in a local area.

Indices by location

South Korea

The Ministry of Environment of South Korea uses the Comprehensice Air-quality Index

(CAI) to describe the ambient air quality based on health risk of air pollution. The index aims to

help the public easily understand air quality level and protect the health of people from air

pollution. - The CAI has values of 0 through 500, which are divided into six categories. The

higher the CAI value, the greater the level of air pollution. - Of values of the five air pollutants,

the highest is the CAI value.
http://en.wikipedia.org/wiki/Ground-level_ozonehttp://en.wikipedia.org/wiki/Ground-level_ozonehttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/Sulfur_dioxidehttp://en.wikipedia.org/wiki/Anticyclonehttp://en.wikipedia.org/wiki/Temperature_inversionhttp://en.wikipedia.org/wiki/Windhttp://en.wikipedia.org/wiki/Air_pollutionhttp://en.wikipedia.org/wiki/Air_pollutionhttp://en.wikipedia.org/wiki/Air_pollutionhttp://en.wikipedia.org/wiki/Air_pollutionhttp://en.wikipedia.org/wiki/Windhttp://en.wikipedia.org/wiki/Temperature_inversionhttp://en.wikipedia.org/wiki/Anticyclonehttp://en.wikipedia.org/wiki/Sulfur_dioxidehttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/Ground-level_ozonehttp://en.wikipedia.org/wiki/Ground-level_ozone


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CAI Description Health Implications

0-50 Good A level that will not impact patients suffering from diseases relatedto air pollution.

51-100 ModerateA level which may have a meager impact on patients in case of

chronic exposure.

101-150Unhealthy for

sensitive groups

A level that may have harmful impacts on patients and members of

sensitive groups.

151-250 Unhealthy

A level that may have harmful impacts on patients and members of

sensitive groups (children, aged or weak people), and also cause the

general public unpleasant feelings.

251-350 Very unhealthyA level which may have a serious impact on patients and members o

sensitive groups in case of acute exposure.

351-500 Hazardous

A level which may need to take emergency measures for patients

and members of sensitive groups and have harmful impacts on the

general public.


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Malaysia

The air quality in Malaysia is reported as the API or Air Pollution Index. Four of the

index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulfur

dioxide) are reported in PM10particulate matter is reported in g/m.

Unlike the American AQI, the index number can exceed 500. Above 500, a state of

emergency is declared in the reporting area. Usually, this means that non-essential government

services are suspended, and all ports in the affected area closed. There may also be a

prohibition on private sector commercial and industrial activities in the reporting area excluding

the food sector.
http://en.wikipedia.org/wiki/Malaysiahttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/State_of_emergencyhttp://en.wikipedia.org/wiki/State_of_emergencyhttp://en.wikipedia.org/wiki/State_of_emergencyhttp://en.wikipedia.org/wiki/State_of_emergencyhttp://en.wikipedia.org/wiki/Particulatehttp://en.wikipedia.org/wiki/Malaysia


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Stock Market Index

A comparison of three major U.S. stock indices: the NASDAQ Composite, Dow Jones

Industrial Average, and S&P 500. All three have the same height at March 2007. Notice the

large dot-com spike on the NASDAQ, a result of the large number of tech. companies on that

index.

A stock market index is a method of measuring a section of the stock market. Many

indices are cited by news or financial services firms and are used as benchmarks, to measure

the performance ofportfolios such as mutual funds.

Types of indices

Stock market indices may be classed in many ways. A 'world' or 'global' stock market

index includes (typically large) companies without regard for where they are domiciled or

traded. Two examples are MSCI World and S&P Global 100.

A national index represents the performance of the stock market of a given nationand

by proxy, reflects investor sentiment on the state of its economy. The most regularly quoted

market indices are national indices composed of the stocks of large companies listed on a

nation's largest stock exchanges, such as the American S&P 500, the Japanese Nikkei 225, and

the British FTSE 100.
http://en.wikipedia.org/wiki/Nasdaq_Compositehttp://en.wikipedia.org/wiki/Dow_Jones_Industrial_Averagehttp://en.wikipedia.org/wiki/Dow_Jones_Industrial_Averagehttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Dot-com_bubblehttp://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Benchmarkinghttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/Mutual_fundhttp://en.wikipedia.org/wiki/MSCI_Worldhttp://en.wikipedia.org/wiki/S%26P_Global_100http://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Nikkei_225http://en.wikipedia.org/wiki/FTSE_100http://en.wikipedia.org/wiki/File:Comparison_of_three_stock_indices_after_1975.svghttp://en.wikipedia.org/wiki/File:Comparison_of_three_stock_indices_after_1975.svghttp://en.wikipedia.org/wiki/FTSE_100http://en.wikipedia.org/wiki/Nikkei_225http://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/S%26P_Global_100http://en.wikipedia.org/wiki/MSCI_Worldhttp://en.wikipedia.org/wiki/Mutual_fundhttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/Benchmarkinghttp://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Dot-com_bubblehttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Dow_Jones_Industrial_Averagehttp://en.wikipedia.org/wiki/Dow_Jones_Industrial_Averagehttp://en.wikipedia.org/wiki/Nasdaq_Composite


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The concept may be extended well beyond an exchange. The Dow Jones Total Stock

Market Index, as its name implies, represents the stocks of nearly every publicly traded

company in the United States, including all U.S. stocks traded on the New York Stock

Exchange (but not ADRs) and most traded on the NASDAQand American Stock

Exchange. Russell Investment Group added to the family of indices by launching the Russell

Global Index.

More specialised indices exist tracking the performance of specific s ectors of the

market. The Morgan Stanley Biotech Index, for example, consists of 36 American firms in

the biotechnology industry. Other indices may track companies of a certain size, a certain type

of management, or even more specialized criteria one index published by Linux Weekly

News tracks stocks of companies that sell products and services based on the Linux operating

environment.

Index versions

Some indices, such as the S&P 500, have multiple versions.[1]These versions can differ

based on how the index components are weighted and on how dividends are accounted for.

For example, there are three versions of the S&P 500 index: price return, which only considers

the price of the components, total return, which accounts for dividend reinvestment, and net

total return, which accounts for dividend reinvestment after the deduction of a withholding

tax. As another example, the Wilshire 4500 and Wilshire 5000 indices have five versions each:full capitalization total return, full capitalization price, float-adjusted total return, float-adjusted

price, and equal weight. The difference between the full capitalization, float-adjusted, and

equal weight versions is in how index components are weighted.

Uses and importance of air pollution index and stock market index

As everyone can see,the air pollution index is use by the government to measure the air

quality index and to detect any pollutants in our countrys air.This is to ensure the air is clean

and safe for us to inhale.Besides that,an early warning can be given to us if the air pollution is tohigh for us to get out of our homes. This warning is given based upon readings and

interpretations of the air pollution index.

As for the stock market index, it is mainly for the business entrepreneurs. This type of

index is used to determine the outcome of a stock market and also the conclusion of a stock

market. The stock market index is important because a countrys economical state sometimes

depend on it.
http://en.wikipedia.org/wiki/United_Stateshttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/American_Depositary_Receipthttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/American_Stock_Exchangehttp://en.wikipedia.org/wiki/American_Stock_Exchangehttp://en.wikipedia.org/wiki/Russell_Investment_Grouphttp://www.russell.com/indexes/characteristics_fact_sheets/global/russell_global_index.asphttp://www.russell.com/indexes/characteristics_fact_sheets/global/russell_global_index.asphttp://en.wikipedia.org/w/index.php?title=Morgan_Stanley_Biotech_Index&action=edit&redlink=1http://en.wikipedia.org/wiki/United_Stateshttp://en.wikipedia.org/wiki/Biotechnologyhttp://en.wikipedia.org/wiki/Linux_Weekly_Newshttp://en.wikipedia.org/wiki/Linux_Weekly_Newshttp://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Stock_market_index#cite_note-0http://en.wikipedia.org/wiki/Stock_market_index#cite_note-0http://en.wikipedia.org/wiki/Stock_market_index#cite_note-0http://en.wikipedia.org/wiki/Weight_functionhttp://en.wikipedia.org/wiki/Dividendhttp://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Wilshire_4500http://en.wikipedia.org/wiki/Wilshire_5000http://en.wikipedia.org/wiki/Wilshire_5000http://en.wikipedia.org/wiki/Wilshire_4500http://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Dividendhttp://en.wikipedia.org/wiki/Weight_functionhttp://en.wikipedia.org/wiki/Stock_market_index#cite_note-0http://en.wikipedia.org/wiki/S%26P_500http://en.wikipedia.org/wiki/Linuxhttp://en.wikipedia.org/wiki/Linux_Weekly_Newshttp://en.wikipedia.org/wiki/Linux_Weekly_Newshttp://en.wikipedia.org/wiki/Biotechnologyhttp://en.wikipedia.org/wiki/United_Stateshttp://en.wikipedia.org/w/index.php?title=Morgan_Stanley_Biotech_Index&action=edit&redlink=1http://www.russell.com/indexes/characteristics_fact_sheets/global/russell_global_index.asphttp://www.russell.com/indexes/characteristics_fact_sheets/global/russell_global_index.asphttp://en.wikipedia.org/wiki/Russell_Investment_Grouphttp://en.wikipedia.org/wiki/American_Stock_Exchangehttp://en.wikipedia.org/wiki/American_Stock_Exchangehttp://en.wikipedia.org/wiki/NASDAQhttp://en.wikipedia.org/wiki/American_Depositary_Receipthttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/New_York_Stock_Exchangehttp://en.wikipedia.org/wiki/United_States


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CONCLUSION

After doing research, answering questions, drawing graphs and some problem solving, I saw

that the usage of index number 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 in

conducting an air-pollution survey. In conclusion, statistics is a daily life essecities. Without it,

surveys cant be conducted, the stock market cant be interpret and many more. So, we should

be thankful of the people who contribute in the idea of statistics.


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REFLECTION

After spending countless hours, days and night to finish this project and also sacrificing my time

video games and mangas in this mid year holiday, there are several things that I can say...

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 excell ing

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 Video Games...

Sacrificing my Facebook...

Sacrificing my Internet...

Sacrificing my Anime...

Sacrificing my Manga...

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 U ADDITIONAL MATHEMATICS...

project work add math 2013 pahang

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