Additional Mathematics Project Work Index Number

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PEARL 1

SELANGOR EDUCATION DEPARTMENT

KOLEJ ISLAM SULTAN ALAM SHAH,KLANG

ADDITIONAL MATHEMATICS PROJECT

WORK 2/2013

NAME:

CLASS:

I/C NUMBER:

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PEARL 2

INTRODUCTION:

OBJECTIVES:

As a student who taking Additional Mathematics is required to carry out a project work while we are in Form 5. This year, the Curriculum Development Division, Ministry of Education has prepared two tasks. We are to choose and complete only ONE task based on their area of interest. Upon completion of the Additional Mathematics Project Work, it is hoped that we will 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 increases interest and confidence;

 prepare ourselves for the demands of their future undertakings and in workplace.

 realise that mathematics is an important and powerful tool in solving real-life problems and hence develope 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.

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PEARL 4

FOREWARD:

First 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 advise, 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,Cik Nursuhailah Azmi 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 from Perlis 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.I’m very grareful finished this project work with success. Thank you.

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PEARL 5

PART 1:INTRODUCTION OF INDEX NUMBER

A) Describe in brief i) Price index

A price index (plural: “price indices” or “price indexes”) is a normalized average (typically a weighted average) of prices for a given class of goods or services in a given region, during a given interval of time. It is a statistic designed to help to compare how these prices, taken as a whole, differ between time periods or geographical locations.

Price indexes have several potential uses. For particularly broad indices, the index can be said to measure the economy's price level or a cost of living. More narrow price indices can help producers with business plans and pricing. Sometimes, they can be useful in helping to guide investment.

History:

No clear consensus has emerged on who created the first price index. The earliest reported research in this area came from Welsh poet Henry Rice Vaughan who examined price level change in his 1675 book A Discourse of Coin and Coinage. Vaughan wanted to separate the inflationary impact of the influx of precious metals brought by Spain from theNew World from the effect due to currency debasement. Vaughan compared labor statutes from his own time to similar statutes dating back to Edward III. These statutes set wages for certain tasks and provided a good record of the change in wage levels. Vaughan reasoned that the market for basic labor did not fluctuate much with time and that a basic laborers salary would probably buy the same amount of goods in different time periods, so that a laborer's salary acted as a basket of goods. Vaughan's analysis indicated that price levels in England had risen six to eightfold over the preceding century.[1]

While Vaughan can be considered a forerunner of price index research, his analysis did not actually involve calculating an index.[1] In 1707 Englishman William Fleetwood created perhaps the first true price index. An Oxford student asked Fleetwood to help show how prices had changed. The student stood to lose his fellowship since a fifteenth century stipulation barred students with annual incomes over five pounds from receiving a fellowship. Fleetwood, who already had an interest in price change, had collected a large amount of price data going back hundreds of years. Fleetwood proposed an index consisting of averaged price relatives and used his methods to show that the value of five pounds had changed greatly over the course of 260 years. He argued on behalf of the Oxford students and published his findings anonymously in a volume entitled Chronicon Preciosum.

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PEARL 6

Formal Calculation:

Given a set of goods and services, the total market value of transactions in in some period would be

where

represents the prevailing price of in period represents the quantity of sold in period

If, across two periods and , the same quantities of each good or service were sold, but under different prices, then

and

would be a reasonable measure of the price of the set in one period relative to that in the other, and would provide an index measuring relative prices overall, weighted by quantities sold.

Of course, for any practical purpose, quantities purchased are rarely if ever identical across any two periods. As such, this is not a very practical index formula.

One might be tempted to modify the formula slightly to

This new index, however, doesn't do anything to distinguish growth or reduction in quantities sold from price changes. To see that this is so, consider what happens if all the prices double between and while quantities stay the same: will double. Now consider what happens if all the quantities double between and while all the prices stay the same: will double. In either case the change in is identical. As such, is as much a quantity index as it is a price index.Various indices have been constructed in an attempt to compensate for this difficulty.

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PEARL 7

ii) What is weightage?

Weightage is common word used in Asia. The meaning for weightage is a weighting factor assigned to compensate for a perceived advantage or ⅟ weight factor or ratio; weight. An example for its usage is: “The admission holds 80% weightage while the interview holds 20% weightage of the admission process”. Weightage also represent as the relative importance of different items.

In a nutshell, weightage can also be said as stake.

iii) What is composite index?

A grouping of equities, indexes or other factors combined in a standardized way, providing a useful statistical measure of overall market or sector performance over time. Also known simply as a "composite".

Usually, a composite index has a large number of factors which are averaged together to form a product representative of an overall market or sector. For example, the Nasdaq Composite index is a market capitalization-weighted grouping of approximately 5,000 stocks listed on the Nasdaq market. These indexes are useful tools for measuring and tracking price level changes to an entire stock market or sector. Therefore, they provide a useful benchmark against which to measure an investor's portfolio. The goal of a well diversified portfolio is usually to outperform the main composite indexes.

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PEARL 8

B) State four ways of weightage representations.Find the examples of the representations using internet or any printed materials.

1) Line Graph 2) Pie Chart A B C D E F Weightage 5 6 8 4 9 3 0 1 2 3 4 5 6 7 8 9

10

The number of staffs in a company

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PEARL 9

3) Percentage

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PEARL 10

PART 2:

We often hear complaints from the public about inflation. It causes an increase in the household expenditure in a family.

The household expenditure for every family is different.

Conjecture:

First of all,I would like to make conjecture about my family expenditure that it will increasing by year.This could be seen as the difference between this year’s average monthly expenditure and the past years are very big. It is big as the years come as the prices of items are increasing gradually. When the prices of items increase, the average monthly average expenditure also increases.

For example when the price of food,entertainment and others increases, the expenditure will also increases. This phenomenon of price increaseing will continue as time goes by.

a) In this case, I would to show my family’s monthly expenditure for the year 2013 to

observe this inflation that happen among us.

Item Average Monthly

Expenditure for the Year 2013 (to the nearest RM)

Percentage of Monthly Expenses (to the nearest %)

Food 600 13

Accommodation (Rental/Loan) 0 0

Transportation (Petrol/Loan/Bus Fare etc) 1200 27 Clothing 400 9 Education 800 18 Recreation 300 7 Utilities (Water/Electricity/Telephone) 600 13 Medication 200 4 Miscellaneous 400 9 TOTAL 4500 100 Table 1

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PEARL 11

If we want to compare the cost of living from one year to another, we have to calculate the price index that involves some of the items mentioned above.

In order to calculate the price index of all the items above, we have to consider the average monthly expenses of any previous year as the base year.

(b) (i)

In this case, I am going to select 2012 as the base year.

By selecting year 2012 as the base year, we can see the increment of price index from year 2012 to 2013.

(ii)

Item Average Monthly Expenses

for the Year 2012 as the Base Year (RM)

Average Monthly Expenses for the Year 2013 (RM) Food 550 600 Accommodation (Rental/Loan) 0 0 Transportation (Petrol/Loan/Bus Fare etc) 900 1200 Clothing 300 400 Education 750 800 Recreation 250 300 Utilities (Water/Electricity/ Telephone) 500 600 Medication 100 200 Miscellaneous 250 400 TOTAL 4100 4500 Table 2

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PEARL 12 (c)(i) Price index is an example of index number which is widely used.

It tells us how the price changes over a fixed period of time.

Formula of price index as shown below:

(a) Q0 = Price of the item at the base time or year

(b) Q1 = Price of the item at specific time

We can calculate the price index of family expenditure of 2013 with base 2012 with this formula .

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PEARL 13 Item Price Indices for the year 2013 Based on

the Year 2012 Weightage Food 109 13 Accommodation (Rental/Loan) 0 0 Transportation (Petrol/Loan/Bus Fare etc) 133 27 Clothing 133 9 Education 107 18 Recreation 120 7 Utilities (Water/Electricity /Telephone) 120 13 Medication 200 4 Miscellaneous 160 9 TOTAL 1082 100 Table 3

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PEARL 14 ii) Then we need to calculate composite index for the average monthly expenditure in the year 2013 based on the year 2012.

The formula of composite index is shown below:

Composite index = 109(13)+133(27)+133(9)+107(18)+120(7)+120(13)+200(4)+160(9) 100 = 127.71 Line Graph 0 200 400 600 800 1000 1200 1400

Average Monthly Expenditure for the year

2013(RM)

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PEARL 15 Blue line : 2012

Grey line: 2013

d) Conclusion:

In the nutshell , I would like to say that the composite index for the average monthly expenditure in year 2013 based on year 2012 increases. This shows that almost all the items in the table have increased. Nevertheless, this shows that my family needs a higher income as. As we can observe, the case of inflation occurs as price of goods increases but the value of money spent remains the same.The government should maintain the economical so that the people can enjoy living in the country without corruption and economic problem involving the family expenditure to stay alive. The government should to prevent cronyism in their life.

It can also be concluded that my family’s expenditure has increased as time passes by based on my findings.

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PEARL 16

PART 3:

My family decided to buy a new television set.

a) I have conducted a survey on the price of the television for two different brands from three different shops. I would like to make a comparison between two modes of payment, namely, cash payment by installment.

Table 4(a) shows the prices of televisions by cash payment in three different shops, namely CBH Electricity,Indera Jaya Enterprise and Kayangan Square whereas Table 4(b) shows the prices of televisions by installment.

Table 4(a) Brand Size of Televisions (inches) Price (RM) Mean Price (RM) Standard Deviation (RM) CBH Electricity Indera Jaya Enterprise Kayangan Square Toshiba 24 599 580 580 586 11 32 899 860 880 880 20 40 1299 1280 1345 1308 33 Samsung 24 599 580 580 586 11 32 899 880 890 890 10 40 1099 1050 1075 1075 26

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PEARL 17 Table 4(b)

Calculate the mean by using the formula below:

Where ∑x = sum of data, n = number of data

To calculate the standard deviation need to use formula as shown below: Brand Size of Televisions (inches) Price (RM) Mean Price (RM) Standard Deviation (RM) CBH Electricity Indera Jaya Enterprise Kayangan Square Toshiba 24 660 588 600 616 39 32 960 876 949 928 46 40 1428 1416 1440 1428 12 Samsung 24 660 588 600 616 39 32 960 888 984 944 50 40 1200 1068 1152 1140 67

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PEARL 18 b) Television that I want to buy.

Based on the findings from part (a) above,I decided to buy Toshiba 32 inches from

Indera Jaya Enterprise by using the cashment payment method.

From the data above, we can see that the price of the television that I have chosen which is RM 860 is below the mean price. This shows that the price is cheaper than the average price for that kind of television. This gives me advantage and chance to save some money. Apart from that, the price is affordable accordance to my family average household expenditure. The price also suits with my budget so I can achieve my budget hopefully with success and great.

Other than that, the standard deviation for that television brand, Toshiba 32 inches is

RM 20 which means the data point are spread out over a large range of values is not so

high. A high standard deviation value means that the average data value is higher which will result in insensibility for the consumers to buy. The television Toshiba 32 inches has reasonable price as the standard deviation is not too high. So,that’s why I choose this television as my decision to have this entertainment.So that I can enjoy my life!

c) The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair

Price Shop Award for the shops above.I am one of the panels for this award.

Based on my findings,the shop that deserves this award is Indera Jaya Enterprise.By considering the value of the mean and the value of standard deviation,here are my justifications. Indera Jaya Enterprise offers prices of television for both brands which below the mean price which the average market price.This shows that Indera Jaya Enterprise is able to offer lower prices for the consumers compared to other shops.Hence,this will benefit the consumers especially for those who come from a low income family. It can be easily to make them become easier

The data of standard deviation for prices of television in Indera Jaya Enterprise is acceptable and can be determined as the standard deviation values are not too high.This shows that the data does not have higher values by both means of payment.So that,we can afford this things for our useful life.

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PEARL 19

PART 4:

a) My family has a fixed monthly income. In order to buy the television, my family needs

to make some adjustment on the various types of expenditure. Here is the revised monthly expenditure.

Expenditure for the Year 2013 (to the nearest RM) Food 600 Accommodation (Rental/Loan) 0 Transportation (Petrol/Loan/Bus Fare etc) 1200 Clothing 400 Education 800 Recreation 300 Utilities (Water/Electricity/Telephone) 600 Medication 100 Miscellaneous 200 Savings 300 TOTAL 4500

So,I choose to pay by cash because my family’s savings is RM 300 per month so that I’ll be able to buy the television Toshiba 32 inches from Indera Jaya Enterprise. So, I need to save the money to RM 860 to make the payment.Then, I need to save money until 3 months so I will achieve RM 900 totally. Then I’ll buy the television with cash payment method.The balance should be RM 40 left and I can save in the savings for the future event.

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PEARL 20 b) Assuming that I have just started working with a monthly salary of RM2500, I intend

to save 10% of my salary every month. Besides, I also plan to contribute some money to my parents monthly.

Expenditure for the Year 2013 (to the nearest RM) Food 400 Accommodation (Rental/Loan) 250 Transportation (Petrol/Loan/Bus Fare etc) 500 Clothing 150 Education 0 Recreation 150 Utilities (Water/Electricity/Telephone) 300 Medication 100 Miscellaneous 100 Savings 250 Contributions to parents 300 TOTAL 2500

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PEARL 21

FURTHER EXPLORATION

For the further exploration,I would like to explore about the price of laptops in the worldwide so that I can manage the survey very well then I can choose which is the better laptops can be worthly to be buy.

The price of laptops on the worldwide nowadays

Brands Type Price(RM)

Acer Aspire V5-431P 1599 Aspire V5-471G 1899 Aspire V3-471 1399 Toshiba Satellite L850 2149 Satellite C800 1399 Satellite L840 1999 Alienware M14x 2999 M17x 4499 M18x 5699

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PEARL 22 Bar Chart

Conclusion:

As a conclude, what I can say that index number is widely used in our daily lives. Price index, composite index, weightage, mean and standard deviation are important for all of us to calculate and compare prices when making a decision to buy something.

This can also be a method to help us to be clever when using money from our salary and prevents overspending on items that are actually cheaper than first thought. If we are good in using index number, it will help us to choose the right item from the right brand at the right price. Sometimes,human thinks clumsy and hard to make decision and now with learning of price index calculation and comparising the item what we want to buy so we can make the best decision and wisely to use in our daily lives.

When,we think this just a ‘rubbish’ so we cannot manage our monthly expenditure as the example wisely.So,think positively,be relax and cool and try to make awesome planning in our lives. Regards.

Cheap Regular Expensive

Acer 1399 1599 1899 Toshiba 1399 1999 2149 Alienware 2999 4499 5699 0 1000 2000 3000 4000 5000 6000

The price of laptops in worldwide

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PEARL 23

REFLECTION:

From conducting the project, a lot of information that I found.. I have learnt that money is very important in our daily life hence agreeing with the saying, “money is not everything but everything is money”. Apart from that, money is so vital for us to ensure the sustainability of our normal life because without money, many things that we want to do cannot be done.Then, I also learned the uses of index number in our life.

Some of the moral values that I practiced during this project are patience, creative and innovative.This project also made me felt more confident to the works and not to give up easily when we could not find the solution for the questions.I also learned to be more discipline because discipline is very important in our life.Without it,we would be just an irresponsible person and no useful for our lovable country,Malaysia.

To conduct a survey on the prices of the television indeed spent a lot of time and energy. Without being patient, the survey might not have been conducted. Other than that, my creativity is developed as I need to do some calculations on the data and to represent it. Besides, I also gain the ability to innovate as I needed to do some modifications on the data in certain circumstances.Without it, how can we be an intelligent person can be respected as students in Malaysia. We can spread the knowledge to each other so the friendship with be tighten and I can enjoy with my friends.

Last but not least, we need to do something that useful for our country so that our country can be more relevant to worldwide that our country can achieve more successful project in worldwide and be the well-known country as ‘Country Success or Great’

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PEARL 24

EVIDENCES OF SURVEYING PLACE:

Kayangan Square(The Store),Kangar

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PEARL 25

REFERENCE:

: http://en.wikipedia.org/wiki/Price_index : http://www.investopedia.com/terms/c/compositeindex.asp : http://www.bumigemilang.com : http://www.scribd.com/umair_pearl : http://www.slidshare.com : http://www.facebook.com : http://www.kisas.org