TitlePage

Acknowledgement

Objectives

Introduction

Part 1

(a)(i) Price index

(ii) Weightage

(iii) Composite index

(b)Weightage representations

Part 2(a)Familys monthly expenditure for year 2013

(b)(i)(ii) Calculating price index

(c)(i)(ii) Composite index for the average monthly expenditure in the year 2013 based on year 2012

(d)Conclusion

Part 3(a) Survey on prices of televisions

(b) Television that I want to buy

(c) Fair Price Shop Award

Part 4(a)Modified monthly expenditure to buy new television

(b)My own monthly expenditure planning

Conclusion

Reflection

ACKNOWLEDGEMENT

The project is theeffort of many parties including mine.Without them, this project would have never been finished. First of all, Iwould like to thank my parents for their support and also myfamily members who made sure that I didnt get distracted doing this project. Thanks to theirunderstanding I wasable tofinish this project with ease.

Next, I would like toexpress my utmost gratitude to my dear additional mathematics teacher, Pn.Husna bt Abdul Hayei for providing the guidelines and explanation aboutthe process of this project work. Her guidance and co-operation is much appreciated.

Not to forget, to all myfriends who were with me during the process of this project especially to Nur Aqilah.I would also like to thank my sister, Afifah for helping me to start my project. Her encouragement and guidance has proven to be most helpful.

Last but not least, I would like toexpress my gratitude to those who have helped medirectly and indirectly, during the course of this project. Thank you all, once again yeah.

OBJECTIVES

The aims of carrying out this project work are:

1. To apply and adapt a variety of problem-solving strategies to solve problems2. To improve thinking skills3. To promote effective mathematical communication4. To develop mathematical knowledge through problem solving in a way that increases students interest and confidence 5. To use the language of mathematics to express mathematical ideas precisely6. To provide learning environment that stimulates and enhances effective learning7. To develop positive attitude towards mathematics

INTRODUCTIONThe Household Expenditure Survey (HES) was the first conducted in the year 1957/58. Beginning 1993/94 it was carried out an interval of live years and the current survey was undertaken in 2009/2010. The survey is covered private households in urban and rural areas. The main objective of HES was to collect information on the level and pattern of consumption expenditure by households on a comprehensive range goods and services to be included in the basket of the Consumer Price Index (CPI). It was also used to represent the expenditure pattern of households in Malaysia. However, over the years, demand for data from the survey has increased and it is now used for several purposes. HES has becomes an invaluable source of information for government and private sectors, researchers and university students. This survey is conducted by using index. Index numbers are meant tostudy the change in the effects of such factorswhich 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 changesin business activityby 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 formeasuring the combined fluctuations in a group related variables. Index numbers may be classified in terms of the variables that they are intended tomeasure. Inbusiness, different groups of variables in the measurement of whichindex number techniques are commonly used are (i) price, (ii) quantity, (iii) valueand (iv) business activity. Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value ofexports and index of business activity, etc

Albert jesse Bowley

PART 1

(a) Describe in brief :i. Price indexAprice index(plural: price indices or price indexes) is a normalizedaverage(typically aweightedaverage) ofpricesfor a given class ofgoodsorservicesin a given region, during a given interval of time. It is astatisticdesigned 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'sprice levelor acost of living. More narrow price indices can help producers with business plans and pricing. Sometimes, they can be useful in helping to guide investment.Some notable price indices include consumer price index,producer price index and GDP deflator.

ii. Weightage

Weightage is common word used in Asia. The meaning for weightage is a weighting factor assigned to compensate for a perceived advantage or weight factor or ratio; weight. Weightage known as the value or quantity assigned to each item in a situation involving several items based on its item. It also can be defined as the value or importance of something when compared with another thing.

An example for its usage is: The admission holds 80% weightage while the interview holds 20% weightage of the admission process. In a nutshell,weightage can also be said as stake.

iii. Composite index

Composite index is a grouping of equities, indexes and other factors combined in standardized way, providing a useful statistical measure of overall marketor sector performance over time. A composite index may also be used in the natural or social sciences to summarize complex or multidimensional data or redundant measures.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.

(b) Ways of weightage representations.

1. Column chart

2. Line chart

3. Pie chart

4. Doughnut chart

PART 2

We often hear complaints from the public about inflation.It cause an increase in thehousehold expenditure in a family. The household expenditure for every family is different. a) My familys monthly expenditure for the year 2013.

ItemAverage Monthly Expenditure for the year 2013 (RM) Percentage of monthly expenses (%)

Food120023

Accommodation80015

Transportation5009

Clothing2004

Education100019

Recreation1002

Utilities60011

Medication60011

Miscellaneous3006

TOTAL5300100

Table 1If we want to compare the cost of living from one year to another, we haveto 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 considerthe 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) ItemAverage monthly expenses for the year 2012 as the base year (RM)Average monthly expenses for the year 2013(RM)

Food13001200

Accommodation800800

Transportation700500

Clothing300200

Education11001000

Recreation100100

Utilities600600

Medication600600

Miscellaneous300300

TOTAL58005300

Table 2

(c) (i)ItemPrice indices for the year 2013 based on the year 2012Weightage

Food92.3123

Accommodation10015

Transportation71.439

Clothing66.674

Education90.9119

Recreation1002

Utilities10011

Medication10011

Miscellaneous1006

TOTAL821.32100

Table 3

(ii) The composite index for my familys average monthly expenditure in the year 2013 based on the selected base year is :

= 23(92.31) +15(100) +9(71.43) +4(66.67) +19(90.91) +2(100) +11(100) +11(100) +6(100)100

= 2123.13+1500+642.87+266.68+1727.29+200+1100+1100+600 100

= 9259.97 100

= 92.60

(d) Conclusion

From my observation, I can conclude that although the price of goods increases, it does not affect my familys average monthly expenses to decrease in this year based on last year.My familys total average monthly expenses in 2012 was more higher than year 2013.This is because my older sister get married on year 2012.This marriage lead to decreases in my familys monthly expenditure in year 2013.

My family used up most money on food and education as food is important in our life. We often buy nutritious food which is quite expensive. Plus, my parents have seven children and still studying in school and college that increases the uses of money in education. Instead, my family used up least money on recreation. My family does not doing much recreation due to busy of works and studies.

PART 3

Your family is planning to buy a new television.

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

Table 4(a) shows the prices of television by cash payment in three differentshops whereas Table 4(b) shows the prices of televisions by installment.

BrandSize of Television (inches)Price (RM)Mean Price(RM)Standard Deviation(RM)

Shop AShop BShop C

Sharp24669758899775.3394.72

3276084894585175.56

401499149915991532.3347.25

Toshiba2456967878767889.00

32739828889818.6761.55

40124912861290127518.46

Table 4(a)

BrandSize of Television (inches)Price (RM)Mean Price(RM)Standard Deviation(RM)

Shop AShop BShop C

Sharp24849988104996283.69

3299010381155106169.30

401659169917891715.6754.26

Toshiba2472478779376831.21

3293696799896725.31

402234227622902266.6723.48

Table 4(b)

(b) ) Based on my findings from part (a) above, I have decided to buy television TOSHIBA with size 32 from Shop A by using the cash payment method.

From the data above, we can see that the price of the television that I have chosen which is RM739 is below the mean price. This shows that the price is cheaper than the average price for that kind of television. Comparing to the television SHARP, we can observe that the price is more expensive even the size of the television is same. Whether in size 24 , 32 or 42, the price is too higher compared to the TOSHIBAs television. My choice gives me advantage and chance to save some money. Apart from that, the price is affordable accordance to my family average household expenditure.

Other than that, the standard deviation for that television brand, TOSHIBA 32 inches is RM 61.55 which means the average data value is not extreme as SHARPs television. A high standard deviation value means that the average data value is extreme which will result in insensibility for the consumers to buy. This is because not all family has higher income.The television TOSHIBA 32 inches has reasonable price as the standard deviation is not too high.

(c) Fair Price Shop Award

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 Shop A. By considering the value of the mean and the value of standard deviation, here are my justifications.

Shop A offers prices of television for both brands which are below the mean price which the average market price even still has one or two price that over the mean. But this is not the problem in fact it is better compared to the others shop. This shows that Shop A 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.

The data of standard deviation for prices of television in Shop A is acceptable and sensible as the standard deviation values are not too high. This shows that the data does not have extreme values by both means of payment.

PART 4(a) My family has a fixed monthly income. In order to buy the television by installment, my family needs to make some adjustments on the various types of expenditure. This is the average monthly expenditure that I had modified in a table.

ItemFixed Average Monthly expenditure (RM)Average Monthly Expenditure for the Year 2013 (to the nearest RM)

Food12001100

Accommodation 800800

Transportation 500450

Clothing200150

Education1000900

Recreation10050

Utilities 600600

Medication600550

Miscellaneous300300

Savings-400

TOTAL53005300

(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 of my salary to my parents every month. ItemAverage Monthly Expenditure for the year 2013 (RM) Percentage of monthly expenses (%)

Food35014

Accommodation30012

Transportation2008

Clothing1004

Education40016

Recreation502

Utilities30012

Medication1506

Miscellaneous1004

Savings25010

Contribution to parents30012

TOTAL2500100

CONCLUSION

As a conclusion, the objectives of this project have been approved. As for me, one of the objectives of this project is to realize that mathematics is an important and powerful tool in solving real-life problems and hence developed positive attitude towards mathematics is approve. It is because in this chapter index number I learn how a good planner in my life is. Its help me how plan my expenditure for my future. As you know, to be a good person in life, we must know how to plan our expenditure and so, we can live in good way.

In part 2, it shows my family expenditure that has not known. So now I know that my family expenditure a bit big but still can adjust how to plan it. Furthermore, in part 3 in this project it tells me how to buy good products that are cheap and quality. Its also teaching us how to choose a shop that sells true and quality products. By comparing three shops, we can know in what shop sold the best price than people to by some product. In part 4, we can also plan a more wise expenditure on various items in the future so that we will not waste our money too much especially on miscellaneous and make the most important items such as food, loan and bills as our priority.

Hopefully my experiences and knowledge that I got by completing this project will be useful for me in the future.

REFLECTIONWhile doing this project, I have spent countless hours doing this project. I realized that thissubject is a compulsory to me. Without it,I cant fulfill my big dreams andwishes.

Additional Mathematics,Are you as easy as a click,Do you become easier as we speak,You are the one I seek,you are the one I need.

Since I ever heard of you, I become afraid of youbut when I know you, you attract me out of the blue.

with you, although it hard to be right,I try my best not to be out of sight,with Teacher Husna to show the light,and practices at nightnow I shall see the light.And it is so bright :)