1. Name : AmirulIkram bin Aslian
I/C No : 960804-10-5667
Class : 5 Anggerik
Teacher : EncikRavinderan
School : SekolahMenegahKebangsaanBandar
UtamaDamansara (4)
Title : Price Index
2. CONTENTS:
Title Page
Acknowledgement
Objectives
Introduction
Part 1 (a)
(i) Index Number
(ii) Weightage
(iii) Composite Index
(b) Weightage Representation
Part 2
(a) Family’s Monthly
Expenditure for year 2013
(b) (i)(ii) Calculating Price
Indexes
(c) (i)(ii) Composite Index for
Average Monthly
Expenditure for 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
Further Explaination
Reflection
3. ACKNOWLEDGEMENT:
First of all, I wish to express gratitude to Allah s.w.t for his guidance and also giving me the
strength to do this project work. Finally, the additional mathematics project work was
successfully completed with the inspiration, the gift and the instruction were given by Him.
Not forgotten my parents for providing everything, such as money, to buy anything
that are related to this project work and their advice, support which are the most needed for
this project. Internet, books, computers and all that. 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, Mr Ravi for guiding me and my friends
throughout this project. We had some difficulties in doing this task, but he taught us patiently
until we knew what to do. He tried and tried to teach us until we understand what we
supposed to do with the project work.
Last but not least, my friends 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.
4. OBJECTIVES:
The aims 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 increases
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
5. Introduction:
A price indexis a normalized average (typicallyaweighted average) of prices for a given class
ofgoods 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 indices 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
Some notable price indices include:
Consumer price index
Producer price index
GDP(Gross Domestic Product) Deflator
History of early price index:
No clear consensus has emerged on who created the first price index. The earliest
reportedresearch in this area came from Welshman Rice Vaughan who examined price level
change in his 1675 book ‘A Discourse of Coin and Coinage’. Vaughan wanted to separate the
inflationaryimpact of the influx of precious metals brought by Spain from the New World
from the effectdue 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 goodrecord of the change in wage levels. Vaughan reasoned that the market
for basic labor did notfluctuate 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
raised six to eightfold over the precedingcentury
While Vaughan can be considered a forerunner of price index research, his analysis did not
actually involve calculating an index. 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 usedhis methods to show that the value of five pounds had
changed greatly over the course of 260years. He argued on behalf of the Oxford students and
published his findings anonymously in a volume entitled ‘ChroniconPreciosum’
6. PART 1 :
a)(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 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 of a legislature) to a particular segment of
the population as a special favor or concession in a proportion abovethat 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) Ways To Represent Weightage
Weightage in a set of data can be represented in certain ways.
1)Bar Chart:
8. Part 2:
a)My Family Expenditure
Items
Average Monthly
Expenditure for the year
2013
(to the nearest RM)
Percentage of monthly
expenses
(to the nearest %)
Food 1250 25
Accommodation
(Rental/Loan)
600 12
Transportation
(Petrol/Loan/Bus fare etc)
250 5
Clothing 250 5
Education 600 12
Recreation 650 13
Utilities
(Water/Electricity/Telephone)
600 12
Medication 500 10
Miscellaneous 300 6
TOTAL 5000 100
Table 1
b)(i)Base year 2012
(ii)Complete Table 2
Items
Average monthly expenses
for the year 2012 as the base
year
(RM)
Average monthly expenses
for the year 2013
(RM)
Food 1000 1250
Accommodation
(Rental/Loan)
500 600
Transportation
(Petrol/Loan/Bus fare etc)
250 250
Clothing 200 250
Education 400 600
Recreation 550 650
Utilities
(Water/Electricity/Telephone)
450 600
Medication 400 500
Miscellaneous 250 300
TOTAL 4000 5000
9. c)(i)
Items Price Indices for the year
2013
Based on the Year 2012
Weightage
Food 125 11
Accommodation
(Rental/Loan)
120 11
Transportation
(Petrol/Loan/Bus fare etc)
100 9
Clothing 125 11
Education 150 13
Recreation 118 11
Utilities
(Water/Electricity/Telephone)
133 12
Medication 125 11
Miscellaneous 120 11
TOTAL 1116 100
Table 3
Formula to calculate price index:
I= × 100
I = Index Number
Q₁= Quantity of specific time
Q₀ = Quantity at base time
(ii)The composite index for my family average monthly expenditure in the year 2013 based
on the year 2012 can be calculated by using this formula below:
Composite index=
W = Weightage
I = Index Number
=
=
=125.09
10. d)Conclusion
The composite index for the average monthly expenditure in year 2013 based on year 2011
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.It can also
be concluded that my family’s expenditure has increased as time passes by based on my
findings.
12. The mean and standard deviation of the data can be calculated using formula
13. b) Based on my findings from part (a) above, I have decided to buy the television Sony,
32 inches from Infinito Graphic 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 RM788 is below the mean
price. This shows that the price ischeaper 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. Other than that, the
standard deviation for that television brand, Sony 32 inches is RM81.65 which means the
average data value is not extreme. A high standard deviation value means that the average
data value is extreme which will result in insensibility for the consumers to buy. The
television Sony 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 Infinito Graphic. By considering the value of the mean and
the value of standard deviation, here are my justifications.Offers prices of television for both
brands which are below the mean price which the Infinito Graphic average market price. This
shows that Infinito Graphic 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 offered from Infinito
Graphic 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. This means that
the shop has put reasonable prices of the televisions.
14. 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.
Items Average Monthly Expenditure for the
Year 2013 (to the nearest RM)
Food 1250
Accomodation
(Rental/Loan)
600
Transportation
(Petrol/Loan/Bus Fare etc)
200
Clothing 200
Education 600
Recreation 400
Utilities (Water/Electricity/Telephone) 600
Medications 500
Miscellaneous 150
Savings 500
TOTAL 5000
Revised Monthly Family Expenditure
From the table above, my family is able to save RM500 per month. By the using cash
payment to buy a television from Infinito Graphic, 40inches which is priced at
RM1599 from Sony. My family will be able to buy the television price after saving
the money for four months, which the amounts of savings will reach RM2000
15. 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.
Items Average Monthly
Expenditure for the Year
2013 (to the nearest RM)
Percentage of Monthly
Expenses (to the nearest
%)
Food 400 16
Accomodation(Rental/Loan) 300 12
Transportation
(Petrol/Loan/Bus Fare etc)
300 12
Clothing 200 8
Education 0 0
Recreation 300 12
Utilities
(Water/Electricity/Telephone)
250 10
Medication 50 2
Miscellaneous 150 6
Savings 300 12
Contributions to my Parents 250 10
TOTAL 2500 100
My monthly Expenditure Budget
Here is my own monthly expenditure budget after getting a job with monthly salary of
RM2500.
16. CONCLUSION:
After doing research, answering questions and some solving problem, I notice that we usually
use index number in our daily life. We can solve our financial problems with ease using price
index and composite index
FURTHER EXPLORATION:
For further investigation, I have chosen to investigate the prices of two superbikes from a
well-known brand, Yamaha and Honda
Brands Model Price (RM)
Honda CBR600RR 74000
CBR1000RR 98000
Yamaha YZF-R6 75000
YZF-R1 97000
*The Honda CBR600RR is compared to the Yamaha YZF-R6 as a supersport motorcycle.
The Honda CBR1000RR is compared to the Yamaha YZF-R1 as a litre motorcycle.
17. REFLECTION:
While I was conducting this project, a lot of information that I had found. I have
learnt how index number appears in our daily life. Apart from that, this project encourages
the student to work together and share their knowledge. It is also encourage student to gather
information from the internet, improve thinking skills and promote effective mathematical
communication. Not only that, I had learned some moral values that I practice. This project
had taught me to responsible on the works that are given to me to be completed. This project
also had made me felt more confidence to do works and not to give easily when we could not
find the solution for the question. I also learned to be more discipline on time, which I was
given about three weeks to complete this project and pass up to my teacher just in time. I also
enjoy doing this project I spend my time with friends to complete this project and it had
tighten our friendship. Last but not least, I proposed this project should be continue because it
brings a lot of moral value to the student and also test the students understanding in
Additional Mathematics.
