Additional Mathematics Project Work 2013

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ADDITIONAL

MATHEMATICS PROJECTWORK 2013

SELANGOR

(PROJECT 2)


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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 possibleto 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 advice 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 result of the change in the constitute variables.

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 withrespect 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. The present

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 ina single variable

with respect to a base.

Composite Index Number


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

group of relative variables with respect to a base.

PART 1

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

Answer :

Price index : an index number expressing the level of a group of commodity pricesrelative to the level of the prices of the same commodities during an arbitrarilychosen base period and used to indicate changes in the level of prices fromone period to another.

Weightage : the assignment of a quota (as of members of a legislature) to a particularsegment of the population as a special favor or concession in a proportionabove that allowable on a strictly numerical basis

(iii) Composite index : A grouping of equities, indexes or other factors combined in a standardizedway, providing a useful statistical measure of overall market or sectorperformance 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 :

Pie chart

Bar graph

Line graph


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Histogram


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PART 2

We 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.

Answer:

Monthlysalary

Number offamily

members

Item

Average MonthlyExpenditure for the

year 2013(to the nearest RM)

Percentage ofmonthly

expenses(to the nearest

%)

RM 6000 5

Food 1200 20.0

Accomodation(Rental / Loan) 240 4.0

Transportation(Petrol/ Loan / Bus

fare etc)600 10.0

Clothing 240 4.0

Education 1500 25.0

Recreation 210 3.5

Utilities(Water / Electricity

/ Telephone)210 3.5

Medication 300 5.0

Miscellaneous 1500 25.0

TOTAL 6000 100


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Table 1

(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 considerthe average monthly expenses of any previous year as the base year.

Select the appropriate year as the base year.

Answer:

ItemAverage Monthly

Expenditure for the baseyear 2008

(RM)

Food 700

Accomodation(Rental / Loan)

200

Transportation(Petrol/ Loan / Bus fare

etc)

450

Clothing 120

Education 1000

Recreation 150

Utilities(Water / Electricity /

Telephone)

180

Medication 200

Miscellaneous 1000

TOTAL 4000


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(ii) Hence, complete Table 2 below:

Answer:

ItemAverage monthly

expenses for the year2008 as the base year

(RM)

Average monthlyexpenses for the

year 2013(RM)

Food 700 1200

Accomodation(Rental / Loan) 200 240

Transportation(Petrol / Loan / Bus fare etc) 450 600

Clothing 120 240

Education 1000 1500

Recreation 150 210

Utilities(Water / Electricity / Telephone) 180 210

Medication200

300

Miscellaneous1000

1500

TOTAL 4000 6000

Table 2


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

Item Price indices for the year2013 based on the year 2008 Weightage

Food 171.43 20.0

Accomodation(Rental / Loan) 120.00 4.0

Transportation(Petrol / Loan / Bus fare etc) 133.33 10.0

Clothing 200.00 4.0

Education 150.00 25.0

Recreation 140.00 3.5

Utilities(Water / Electricity / Telephone) 116.67 3.5

Medication 150.00 5.0

Miscellaneous 150.00 25.0

TOTAL 1331.43 100

Table 3

Formula to calculate price index :


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( 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 :

= (171.43 X 20) + (120 X 4) + (133.33 X 10) + (200 X 4) + (150 X 25) + (140 X 3.5) +

(116.67 X 3.5) +(150 X 5) + (150 X 25)

(20 + 4 + 10 + 4 + 25 + 3.5 + 3.5 + 5 + 25)

= 151.90

(d) Make a conclusion about your family's expenditure based on your findings.

Answer :

Based on the findings, I found that the average expenses for current year is higher than

the base year 2008. We spent a total of RM1200 for food in 2013 compared to only

RM700 in 2008. Other expenses such as accommodation, utilities, transportation,

clothing, education, recreation, and medications also increase compared to the year

2008. This is due to the high inflation rate in 2008. After the year 2008, daily expensesfor our family had increased due to the increasing of the prices of raw materials.


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PART 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 different

brands

from three different shops. You would like to make a comparison between two

modes of payment, namely, cash payment and payment by installment.

Table 4 (a) shows the prices of televisions by cash payment in three differentshops

whereas Table 4(b) shows the prices of televisions by instalment.Complete Table 4 (a) and 4(b) using the data you obtained.

Answer:

BrandSize of

Television(inches)

Price (RM)

MeanPrice(RM)

StandardDeviation

(RM)Hup

LiongShop

RamliElectonics

&Hardware

KedaiElektrik

Chong

TS24 988 788 888 888.00 81.6532 1788 1599 1690 1693.33 1685.61

40 2888 2500 2300 562.67 2512.02

SH

24 788 699 999 828.67 125.78

32 969 848 1200 1005.67 1010.70

40 1288 1269 1499 1352.00 104.23

Table 4(a)


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BrandSize of

Television(inches)

Price (RM)

MeanPrice(RM)

StandardDeviation

(RM)HupSeng

RamliElectronic

s &Hardware

KedaiElektrikChong

TS

24 1383.2 945.6 1154.4 1161.07 178.69

32 2503.2 1918.8 2197.0 2206.33 238.70

40 4043.2 3000.0 2990.0 3344.40 494.14

SH

24 1103.2 838.8 1298.7 1080.23 188.47

32 1356.6 1017.6 1560.0 1311.40 223.73

40 1803.2 1522.8 1948.7 1758.23 176.79

Table 4(b)

The mean and standard deviation of the data can be calculated using formula :


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

Answer:

I want to buy a size 32 inch TS television. This is because there are only fivemembers in my family and only requires medium-sized television for our livingroom. I choose this brand because I am confident of its quality as our family haslong been using this brand for other electrical appliances in our home. Althoughthe brand TS is more expensive than the brand SH, our family still can afford tobuy it. I plan to buy from Ramli Electronics & Hardware store because they offer2 years of warranty. In addition, they also offer the lowest price of televisionscompared to the other two shops.

(c) The Ministry of Domestic Trade and Consumer Affairs wishes to present the FairPriceShop Award for one of the above shops. If you are one of the panels for this

award,determine the shop that deserve the award. Do you consider the value of the

mean andthe value of standard deviation in making your decision? Give your justifications.

Answer:

If I am one of the panel for the award, I would prefer Ramli Electronics &Hardware shop because the mean price of all types of television for both brandsis the lowest compared to the other two shops. Standard deviation for thetelivisons at the shop is also the lowest. It shows that the prices of televisionoffered by the Ramli Electronics & Hardware shop is reasonable and affordable.


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PART 4

(a) Your family has a fixed monthly income. In order to buy the television, yourfamily 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.

ItemAverage MonthlyExpenditure (RM)

Modifiedexpenditure (RM)

Food 1200 1200

Accomodation(Rental / Loan) 240 240

Transportation(Petrol/ Loan /Bus fare etc)

600 500

Clothing 240 50

Education 1500 1300

Recreation 210 100

Utilities(Water /

Electricity /Telephone)

210 210

Medication 300 150

Miscellaneous 1500 750

Television - 1500

TOTAL 6000 6000


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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 items such as

savings and contributions to your parents.

ItemAverage Monthly Expenditure

(RM)

Food 400

Accomodation(Rental / Loan) 300

Transportation(Petrol/ Loan / Bus fare etc) 200

Clothing 100

Education 100

Recreation 50

Utilities(Water / Electricity / Telephone) 100

Medication 100

Savings 250

Parents 600

Miscellaneous 300TOTAL 2500

Additional Mathematics Project Work 2013

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