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The aim of carrying out this project work are:
-to apply and adapt a variety of problem-solving strategies to solve problems
-to improve thinking skills
-to promote effective mathematical communication
-to develop mathematical knowledge through problem solving in a way that increase
students interest and confidence
-to use the language of mathematics to express mathematical ideas precisely
-to provide learning environment that stimulates and enhances effective learning
-to develop positive attitude towards mathematics
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First and foremost, I would like to thank my Additional Mathematic teacher, Pn
Lee Wee Leng as she gives us important guidance and commitment during this project
work. She has been a very supportive figure throughout the whole project.
I also would like to give thanks to all my friends for helping me and always
supporting me to help complete this project work. The have done a great job at
surveying various shops and sharing information with other people including me.
Without them this project would never have had its conclusion.
For their strong support, I would like to express my gratitude to my beloved
mother also for supplying the equipments and money needed for the resources to
complete this project. They have always been by my side and I hope they will still be
there in the future.
Last but not least, I would also like to thank all the nice shop keepers, stuff and
citizens for helping me collect the much needed data and statistic for this. Not forgetting
too all the other people who were involve directly or indirectly towards making this
project a reality.
I really appreciate all the help I have got. Again, thank you very much!
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NO. Content Page
1 Objectives
2 Acknowledgement
3 Introduction
4 Part 1
Part 1(a)(i) Part 1(a)(ii) Part 1(a)(iii) Part 1(b)5 Part 2 Part 2(a) Part 2(b)(i) Part 2(b)(ii) Part 2(c)(i) Part 2(c)(ii) Part 2(d)
6 Part 3
Part 3(a) Part 3(b) Part 3(c)
7 Part 4
Part 4(a) Part 4(b)
8 Reflection
9 Reference
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H istory of I ndex Number
Index numbers are meant to study the change in the effects of such factorswhich cannot be
measured directly. According to Bowley, Index numbers are usedto measure the changes in
some quantity which we cannot observe directly. For example, changes in business activity
in a country are not capable of directmeasurement but it is possible to study relative changes
in business activity bystudying the variations in the values of some such factors which affect
businessactivity, and which are capable of direct measurement.Index numbers are commonly
used statistical device for measuring thecombined fluctuations in a group related variables. If
we wish to compare the pricelevel 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 productionor industrial
production with that at the time of independence. Here again, we haveto consider all items of
production and each item may have undergone a differentfractional 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 variablesover 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 classifiedin terms of the variables that they areintended to measure. In business, different groups of
variables in themeasurement 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 mainlyinterested in index numbers of prices
showing changes with respect to time,although methods described can be applied to other
cases. In general, thepresent 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 iscalled the base
period.
I ndex Numbers
Index numbers are statistical measures designed to show changes ina variable or group of
related variables with respect to time, geographiclocation or other characteristics such as
income, profession, etc. A collectionof index numbers for different years, locations, etc., is
sometimes called anindex series.
Simple Index Number
A simple index number is a number that measures a relative change ina single variable withrespect to a base.
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Composite I ndex Number
A composite index number is a number that measures an averagerelative 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 :
(i) Price index : an index number expressing the level of a group ofcommodity prices relative tothe level of the prices of the same commodities during an arbitrarily 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 ofa legislature) to a particular
segment of the population as a special favour 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 market or sector performance over
time.
(b) State four ways of weightage representations. Find the examples of the representations
using internet or any printed materials.
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Answer :
Ways to represent weightage :
1) Pie chart
2) Bar graph
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3) Line graph
4) Histogram
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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.
a) Complete Table 1 for your family's monthly expenditure for the year 2013.
Answer:
Monthly
salary
Number of
family members
Item
Average Monthly
Expenditure for the
year 2013
(to the nearest RM)
Percentage of
monthly 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
Table 1
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(b) 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.
(i) 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.
Select the appropriate year as the base year.
Answer:
Item
Average Monthly
Expenditure for the base
year 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:
Item
Average monthly
expenses for the year 2008as the base year
(RM)
Average monthly
expenses for the year2013
(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 year 2013
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 expenditure
inthe 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 in2008. 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 expenses for 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 twomodes of payment, namely, cash payment and payment by instalment .
Table 4 (a) shows the prices of televisions by cash payment in three different shops
whereas Table 4(b) shows the prices of televisions by instalment.
Complete Table 4 (a) and 4(b) using the data you obtained.
Answer:
Brand
Size of
Television
(inches)
Price (RM)
Mean
Price
(RM)
Standard
Deviation
(RM)Hup
Liong
Shop
Ramli
Electonics
&
Hardware
Kedai
Elektrik
Chong
TS
24 988 788 888 888.00 81.65
32 1788 1599 1690 1693.33 1685.61
40 2888 2500 2300 562.67 2512.02
SH 24 788 699 999 828.67 125.7832 969 848 1200 1005.67 1010.70
40 1288 1269 1499 1352.00 104.23
Table 4(a)
Brand
Size of
Television
(inches)
Price (RM)
Mean
Price
(RM)
Standard
Deviation
(RM)
Hup Seng
Ramli
Electronics&
Hardware
Kedai
Elektrik
Chong
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)
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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. Give
your 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 five
members in my family and only requires medium-sized television for our living room.
I choose this brand because I am confident of its quality as our family has long been
using this brand for other electrical appliances in our home. Although the brand TS is
more expensive than the brand SH, our family still can afford to buy it. I plan to buy
from Ramli Electronics & Hardware store because they offer 2 years of warranty. In
addition, they also offer the lowest price of televisions compared to the other two
shops.
(c) The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair PriceShop 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 and
the 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 brands is the lowest
compared to the other two shops. Standard deviation for the telivisonsat the shop is
also the lowest. It shows that the prices of television offered 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, your
family needs to make some adjustment on the various types of expenditure.
[You can choose to pay by cash or by instalment]
Show the average monthly expenditure that you have modified in a table.
ItemAverage Monthly
Expenditure (RM)
Modified expenditure
(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.
Item Average 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 300
TOTAL 2500
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In the process of conducting this project, I have learnt that perseverance pays off,
especially when you obtain a just reward for all your hard work. For me, succeeding in
completing this project work has been reward enough. I have also learnt that mathematics is
used everywhere in daily life, from the most simple things like daily expenses and choosing
size of electronic devices, prediction and estimation of price of products in the market.
Besides that, I get to communicate with friends by discussing this project. We used the time
wisely and finished up the project in time.
The co-operation among everyone made our relationship getting closer. And also
parents who helped me while Im having problem with the project. I get to build relationships
with my parents. While I was conducting the project, I had learned many moral values that I
practice. This project work had taught me to be more confident when doing something
especially the homework given by the teacher. I also learned to be a disciplined type of
student which is always sharp on time while doing some work, complete the work by myself
and my friends and researching the information from the internet. I also felt very enjoy when
making this project.
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