Additional Mathematics Project Work 2/2013 (Index Number) SELANGOR. FORM 5

7/28/2019 Additional Mathematics Project Work 2/2013 (Index Number) SELANGOR. FORM 5.

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SMK SEKSYEN 10 KOTA DAMANSARA

ADDITIONAL M ATHEMATICS

P ROJECT W ORK 2013

(P ROJECT 2)


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OBJECTIVE

We students taking Additional Mathematics are required to carry out a projectwork while we are in Form 5. This year the Curriculum Development Division,Ministry of Education has prepare two task for us. We are required to choose andcomplete only one task base on our area of interest. This project can be done ingroups or individually, but each of us is expected to submit an individually writtenreport. Upon completion of the valuable experience and able to:

Apply and adapt a variety of problem solving strategy to solve routine andno routine problems

Acquire effective mathematical communication through oral or writing, andto use the Language of Mathematics to express mathematical ideas correctlyand precisely

Realize that mathematic is an important and powerful tool in solving real-life problems and hence, develop positive attitude towards math

Prepare ourselves for the demand of our future in managing our householdexpenditure


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P ART 1

(a ) Describe in brief (i) price index,(ii) weightage,

(iii) composite index.

Answer:

(i) Price Index: an index number expressing the level of a group of commodity prices

relative to the level of the prices of the same commodities during anarbitrarily chosen base period and used to indicate changes in the level of

prices from one period to another.

(ii) Weightage: the assignment of a quota (as of members of a legislature) to a

particular segment of the population as a special favor or concession in a proportion above that allowable on a strictly numerical basis

(iii) Composite Index: A grouping of equities, indexes or other factors combined in a

standardized way, providing a useful statistical measure of overall marketor sector performance over time.


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

Answer:

Ways to represent weightage:

1. Bar graph

2. Line graph


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3. Pie chart


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INTRODUCTION History of Index Number

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 numbersare 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 variationsin the values of some such factors which affect business activity, and which are capableof direct measurement. Index numbers are commonly used statistical device for measuring the combined fluctuations in a group related variables. If we wish to comparethe price level of consumer items today with that prevalent ten years ago, we are notinterested 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 toconsider all items of production and each item may have undergone a different fractionalincrease (or even a decrease). How do we obtain a composite measure. This compositemeasure is provided by index numbers which may be defined as advice for combining thevariations that have come in group of related variables over a period of time, with a viewto obtain a figure that represents the result of the change in the constitute variables. Indexnumbers 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)businessactivity. Thus, we have index of wholesale prices, index of consumer prices, indexof industrial output, index of value of exports and index of business activity, etc. Here weshall be mainly interested in index numbers of prices showing changes with respect totime, although methods described can be applied to other cases. In general, the presentlevel of prices is compared with the level of prices in the past. The present period iscalled the current period and some period in the past is called the base period.

Index NumbersIndex numbers are statistical measures designed to show changes in a variable or groupof related variables with respect to time, geographic location or other characteristics suchas 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 ina single variablewith respect to a base.

Composite Index Number A composite index number is a number that measures an average relative changes in agroup of relative variables with respect to a base.


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P ART 2We often hear complaints from the public about inflation. It causes an increase in thehousehold expenditure in a family. The household expenditure for every family isdifferent.

a) Complete Table 1 for your family's monthly expenditure for the year 2013.

Item Average MonthlyExpenditure for the year

2013(to the nearest RM)

Percentage of monthly expenses(to the nearest %)

Food 1200 30

Accommodation(Rental/Loan) 1000 25

Transportation(Petrol/Loan/Bus fare etc)

500 12.5

Clothing 200 5

Education 300 7.5

Recreation 300 7.5

Utilities(Water/Electricity/Telephone)

300 7.5

Medication 100 2.5

Miscellaneous 100 2.5

TOTAL 4000 100


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

(i) In order to calculate the price index of all the items above, we have to consider theaverage monthly expenses of any previous year as the base year. Select theappropriate year as the base yea r.

Answer:

Item Average Monthly Expenditure for theyear 2011

(RM)Food 1000

Accommodation

(Rental/Loan)

800


400

Clothing 100

Education 300

Recreation 300

Utilities(Water/Electricity/

Telephone)

200

Medication 200

Miscellaneous 100

TOTAL 3400


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(ii) Hence, complete the Table 2 below:

Item Average MonthlyExpenditure for the year

2011 as the base year (RM)

Average monthlyexpanses for the year

2013(RM)

Food 1000 1200

Accommodation(Rental/Loan)

800 1000

Transportation

(Petrol/Loan/Bus fareetc)

400 500

Clothing 100 200

Education 300 300

Recreation 300 300

Utilities(Water/Electricity/

Telephone)

200 300

Medication 200 100

Miscellaneous 100 100

TOTAL 3400 4000

Table 2


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(c)(i) Complete Table 3 based on the above information.

Item Price indices for the year 2013 based on year 2011

Weightage

Food 120 11.76


125 12.25


125 12.25

Clothing 200 19.61

Education 100 9.80

Recreation 100 9.80


100 9.80

Medication 50 4.90

Miscellaneous 100 9.80

TOTAL 1020 100

Table 3

Formula to calculate price index:


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(c)(ii) Hence, calculate the composite index for the average monthly expenditurein the year 2013 based on the selected base year.

Answer:

Formula to calculate composite index:

Composite Index= (120 X 11.76) + (125 X 12.25) + (125 X 12.25) + (200 X 19.61) +

(100 X 9.80) + (100 X 9.80) + (100 X 9.80) + (50 X 4.90) + (100 X 9.80)

100

=125.61

(d) Make a conclusion about your familys expenditure based on your findings.

Answer:

Based on my own findings, I found that my familys average monthly expenseshave increase from base year 2011 to current year 2013. In 2011, my family onlyspent a total of RM1200 but it has increase to RM1200 in year 2013. Other itemssuch as accommodation, transportation and clothing have also increased. Due tothe high inflation rate in year 2011 and economic down-turns, our average monthlyexpenses has increased.


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P ART 3

Your family is planning to buy a new television set.(a) You have conducted a survey on the price of the television for two differ

ent brands from three different shops. You would like to make acomparison between two modes of payment, namely, cash payment and payment by installment.

Table 4 (a) shows the prices of televisions by cash payment in threedifferent shops whereas Table 4 (b) shows the prices of televisions byinstallment.

Complete Table 4 (a) and 4 (b) using the data you obtained.

Answer:

BrandSize of

Television(inches)

Price (RM) MeanPrice(RM)

StandardDeviation

(RM)Seng Hing

ShopAlexs E-Shop

KedaiElectrik Halim

FSH24 489 589 500 526 44.77

32 788 888 850 842 41.23

40 1397 1600 1569 1522 89.29

LH24 528 688 589 602 62.82

32 888 988 950 942 41.21

40 1500 1869 1764 1711 155.24

Table 4 (a)


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BrandSize of

Television(inches)

Price (RM) MeanPrice(RM)

StandardDeviation

(RM)SengHingShop

Alexs E-Shop

KedaiElectrik Halim

FSH24 480 588 498 522 47.24

32 780 876 840 832 39.60

40 1392 1584 1560 1512 85.42

LH24 528 692 576 592 112.60

32 876 972 936 928 39.60

40 1488 1860 1752 1700 156.26

Table 4(b)

Formula to calculate mean:


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Formula to calculate standard deviation:

(b) Determine the brand and size of the television that you have decided to buy. Give your reasons based on the findings from part ( a ) above.

Answer:

I decide to buy a 32 inch FSH television. The size of the television is just theright size for my family of five. Moreover, it is cheaper compare to LH tv.Despite being cheaper, the quality is trustworthy for us because our familyhas been using this brand for other electrical appliances in our home. I will

buy the television from Seng Hing Shop because they offer a two year warranty. Not only that, they also offer the lowest price of televisionscompare to the other two shops.


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(c) The Ministry of Domestic Trade and Consumer Affairs wishesto present the Fair Price Shop Award for one of the above shops. If youare one of the panels for this award, determine the shop that deservesthe award. Do you consider the value of the mean and the value of

standard deviation in making your decision? Give your justifications.

Answer:

If I am one of the panels for this award, I will consider the value of meanand the value of standard deviation. I think Seng Hing Shop shoulddeserve this award because the mean price for both FSH and LH televisionare the lowest compare to the other two shops. In addition, the standard

deviation value is also the lowest. It shows that the prices offered by SengHing Shop are more reasonable and standardized according to the marketvalue. The prices offered are also more consumer-friendly.


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P ART 4(a) Your family has a fixed monthly income. In order to buy the television, your

family needs to make some adjustment on the various types of expenditure.

[You can choose to pay by cash or by installment] Show the average monthly expenditure that you have modified in a table.

Item Average MonthlyExpenditure

(RM)

ModifiedExpenditure

(RM)Food 1200 1000


1000 1000


500 300

Clothing 200 100

Education 300 200

Recreation 300 200


300 100

Medication 100 100

Miscellaneous 100 100

Television - 900

TOTAL 4000 4000


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(b) Assuming you have just started working with a monthly salary of RM2 500. You intend to save 10% of your salary every month.Plan your monthly expenditure as in Table 1 above and add other itemssuch as savings and contributions to your parents.

Item Average MonthlyExpenditure

(RM)Food 400


850


300

Clothing 50

Education 100

Recreation 100


150

Medication 50

Miscellaneous 50

Savings 250

Contribution (parents) 200

TOTAL 2500

Documents

Additional Mathematics Project Work 2/2013 (Index Number) SELANGOR. FORM 5