Add Maths Project 2/2013 Full

7/28/2019 Add Maths Project 2/2013 Full

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NAME: PUNITHAN S/O ILANGOVAN

NO.I/C: 960726-10-6663

CLASS: 5P

TEACHER: MR. LEE EE IA


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CONTENT

CONTENT PAGE

ACKNOWLEDGEMNT

OBJECTIVES

INTRODUCTION

PART 1

PART 2

PART 3

PART 4

CONCLUSION

REFLECTION


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ACKNOWLEDGEMENT

The project is the effort of many parties including mine. Without them, this

project would have never been finished. First of all, I would like to thank myparents for their support and also my Family members who made sure that I didnt

get distracted doing this project. Thanks to their understanding I was able to finishthis project with ease.

Next, I would like to express my utmost gratitude to my dear additional

mathematics teacher, En. Lee Ee Ia for providing the guidelines and explanationabout the process of this project work. His guidance and co-operation is much

appreciated.

Not to forget, to all my friends who were with me during the process of thisproject especially to Ong Ti Sien .I would also like to thank Loi Seng Hou for

helping me to start my project. His encouragement and guidance has proven to bemost helpful.

Last but not least, I would like to express my gratitude to those who have

helped me directly and indirectly, during the course of this project. Thank you all,once again.


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Objectives

The aims of carrying out this project work are :

1. To apply and adapt a variety of problem-solving strategies to solve problems

2. To improve thinking skills

3. To promote effective mathematical communication

4. 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 precisely

6. To provide learning environment that stimulates and enhances effectivelearning

7.

To develop positive attitude towards mathematics


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IntroductionThe Household Expenditure Survey (HES) was the first conducted in the

year1957/58. 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 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 possible to 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. Index numbers may be classified interms 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

Albert Jesse Bowley


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PART 1

(a) Describe in brief :

i. Price index

A price index ( plural: priceindices orpriceindexes) is a normalized

average (typically a weighted average)of prices for a given class ofgoods orservices in a

given region, during a given interval of time. It is a statistic designed to help to comparehow 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'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 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

holds20% weightage of the admissionprocess. In a nutshell, weightage can also be said

at 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 market

or 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 groupingof 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 investors

portfolio. The goal of a well diversified portfolio is usually to outperform the main

composite indexes.
http://en.wikipedia.org/wiki/Averagehttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Good_(economics)http://en.wikipedia.org/wiki/Service_(economics)http://en.wikipedia.org/wiki/Statistichttp://en.wikipedia.org/wiki/Price_levelhttp://en.wikipedia.org/wiki/Cost_of_livinghttp://en.wikipedia.org/wiki/Cost_of_livinghttp://en.wikipedia.org/wiki/Price_levelhttp://en.wikipedia.org/wiki/Statistichttp://en.wikipedia.org/wiki/Service_(economics)http://en.wikipedia.org/wiki/Good_(economics)http://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Weighted_meanhttp://en.wikipedia.org/wiki/Average


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(b) Ways of weightage representations

1. Column chart

2. Line chart

weightage

weightage


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3. Pie chart

4. Doughnut chart

Weightage

Food

Accommodation

Transportation

Clothing

Education

Recreation

Weightage

Food

Accommodation

Transportation

Clothing

Education

Recreation


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PART 2

We often hear complaints from the public about inflation.It cause an increase in the

household expenditure in a family.

The household expenditure for every family is different.

a)My familys monthly expenditure for the year 2013.

Item Average Monthly Expenditurefor the year 2013 (RM) Percentage of monthlyexpenses (%)

Food 1200 23

Accommodation 800 15

Transportation 500 9

Clothing 200 4

Education 1000 19

Recreation 100 2

Utilities 600 11

Medication 600 11

Miscellaneous 300 6

TOTAL 5300 100

Table 1

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.

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.

(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)

Item Average monthly expenses for

the year 2012 as the base year

(RM)

Average monthly expenses for

the year 2013

(RM)

Food 1300 1200



Clothing 300 200

Education 1100 1000

Recreation 100 100

Utilities 600 600Medication 600 600

Miscellaneous 300 300

TOTAL 5800 5300

Table 2


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(c) (i)

Item Price indices for the year 2013

based on the year 2012

Weightage

Food 92.31 23


Transportation 71.43 9

Clothing 66.67 4Education 90.91 19

Recreation 100 2

Utilities 100 11

Medication 100 11

Miscellaneous 100 6

TOTAL 821.32 100

Table 3

(ii)The composite index for my familys average monthly expenditure in the year 2013 basedon 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 myfamilys 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.


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PART 3

Your family is planning to buy a new television.

(a) I have conducted a survey on the price of the television for two

different brands from three different shops.I would like to makecomparison between the two modes of payment,namely,cash payment

and payment by installment

Table 4(a) shows the prices of television by cash payment in three different

shops whereas Table 4(b) shows the prices of televisions by installment.

Brand

Size of

Television

(inches)

Price (RM)

Mean Price

(RM)

Standard

Deviation

(RM)Shop A Shop B Shop C

Sharp

24 669 758 899 775.33 94.72

32 760 848 945 851 75.56

40 1499 1499 1599 1532.33 47.25

Toshiba

24 569 678 787 678 89.00

32 739 828 889 818.67 61.55

40 1249 1286 1290 1275 18.46

Table 4(a)

Brand

Size of

Television

(inches)

Price (RM)

Mean Price

(RM)

Standard

Deviation

(RM)Shop A Shop B Shop C

Sharp

24 849 988 1049 962 83.69

32 990 1038 1155 1061 69.30

40 1659 1699 1789 1715.67 54.26

Toshiba

24 724 787 793 768 31.21

32 936 967 998 967 25.31

40 2234 2276 2290 2266.67 23.48

Table 4(b)


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(b) Based on my findings frompart (a) above, I have decided to buy television TOSHIBA with

size 32 from Shop Aby using the cash payment method.

From the data above, we can see that the price of the television that I have chosen which isRM739 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 priceis 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 ininsensibility 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 ofstandard deviation, here are my justifications.

Shop A offers prices of television for both brands which are below the mean price which theaverage 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 consumersespecially 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.


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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.

Item Fixed Average Monthly

expenditure (RM)

Average MonthlyExpenditure for the

Year 2013 (to the

nearest RM)

Food 1200 1100



Clothing 200 150

Education 1000 900

Recreation 100 50

Utilities 600 600Medication 600 550

Miscellaneous 300 300

Savings - 400

TOTAL 5300 5300

(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 myparents every month.

Item Average Monthly

Expenditure for the year

2013 (RM)

Percentage of monthly

expenses (%)

Food 350 14



Clothing 100 4

Education 400 16

Recreation 50 2

Utilities 300 12

Medication 150 6

Miscellaneous 100 4Savings 250 10

Contribution to parents 300 12

TOTAL 2500 100


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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 animportant and powerful tool in solving real-life problems and hence developed

positive attitude towards mathematics is approve. It is because in this chapter indexnumber 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 knowhow 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 andquality 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 wiseexpenditure 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 asfood, loan and bills as our priority.

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


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REFLECTIONWhile doing this project, I have spent countless hours doing this project. I realized

that this subject is a compulsory to me. Without it, I cant fulfill my big dreams

and wishes.

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 you

but 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 Mr. Lee to show the light,

and practices at night

now I shall see the light.

And it is so bright :)

Add Maths Project 2/2013 Full

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