additional mathematics project (2013)(malaysia)

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ADDITIONALMATHEMATICS

PROJECT WORK

2/2013 (SELANGOR)

NAME: Tan Jai LedI/C NUMBER:

ANGKA GILIRAN:

SCHOOL: SMJK YU HUA

DATE: 15th

June 2013



CONTENTS

Num Title Page1 Acknowledgement 12 Objectives 23 Introduction: History of Index

Number3-4

4 Part 1 Questions(a)(b)

4-545


(c)(d)

6-86

6-7

7-88

6 Part 3 Questions(a)(b)(c)

9-109

1010


11-1211

11-128 Further Exploration 13-169 Conclusion 17

10 Reflection 17



ACKNOWLEDGEMENT

I would like to thank my teacher Mr Thean for helping mefinish this project. He has provided me with a lot of information abouthow to do this project perfectly.

I would also like to thank my parents for helping me finish myAdd Math project. They help me by sending me to various shops sothat I can ask about the prices of television and collect data for my

project. They also provided me with our monthly expenses so that Ican fill the table provided.

Lastly, I would like to thank my friends for cooperating with methroughout doing the project. They exchange information with me sothat we can do better together.



Introduction (History of Index Number)

Index numbers are meant to study the change in the effects of suchfactors which cannot be measured directly. According to Bowley, Index

numbers are used to measure the changes in some quantity which we cannotobserve directly´. For example, changes in business activity in a country are notcapable of direct measurement but it is possible to study relative changes in

business activity by studying the variations in the values of some such factorswhich affect business activity, and which are capable of direct measurement.

Index numbers are commonly used statistical device for measuringthe 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 arenot interested in comparing the prices of only one item, but in comparing somesort of average price levels. We may wish to compare the present agricultural

production or industrial production with that at the time of independence. Hereagain, we have to consider all items of production and each item may haveundergone a different fractional increase (or even a decrease). How do weobtain a composite measure This composite measure is provided by indexnumbers which may be defined as advice for combining the variations that havecome in group of related variables over a period of time, with a view to obtain afigure that represents the result of the change in the constitute variables.

Index numbers may be classified in terms of the variables that theyare intended 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 indexof wholesale prices, index of consumer prices, index of industrial output, indexof value of exports and index of business activity, etc. Here we shall be mainly

interested in index numbers of prices showing changes with respect 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 calledthe base period.



Index Numbers

Index numbers are statistical measures designed to show changes in a variableor group of related variables with respect to time, geographic location or other

characteristics such as income, profession, etc. A collection of index numbersfor 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 in a singlevariable with respect to a base.

Composite Index Number

A composite index number is a number that measures an average relativechanges in a group of relative variables with respect to a base.

PART 1

(a) Describe in brief(i) Price index

an index number expressing the level of a group ofcommodity prices relative to the level of the prices of thesame commodities during an arbitrarily chosen base periodand 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) toa particular segment of the population as a special favor

or concession in a proportion above that allowable on astrictly numerical basis (iii) Composite index

A grouping of equities, indexes or other factors combined ina standardized way, providing a useful statistical measure ofoverall market or sector performance over time.



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

(ii) Bar graph

(iii) Line Graph

(iv) Histogram



PART 2

We often hear complaints from the public about inflation. It causes an increasein 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 year2013.

ITEM Average MonthlyExpenditure for the

year 2013(to the nearest RM)

Percentage ofmonthly expenses(to the nearest %)

Food 700 19Accommodation (Rental/ Loan) 500 14

Transportation(Petrol/Loan/Bus fare etc)

500 14

Clothing 100 3Education 500 14Recreation 200 6

Utilities(Water/Electricity/Telephone)

300 8

Medication 300 8Miscellaneous 500 14

TOTAL 3600 100

b) If we want to compare the cost of living from one year to another, wehave to calculate the price index that involves some of the itemsmentioned above.

(i) In order to calculate the price index of all the items above, wehave to consider the average monthly expenses of any previousyear as the base year. Select the appropriate year as the base year.

Item Average Monthly Expenditure forthe year 2012

(to the nearest RM)Food 700

Accommodation (Rental/ Loan) 1300Transportation

(Petrol/Loan/Bus fare etc)700



Clothing 100Education 500Recreation 500

Utilities

(Water/Electricity/Telephone)

400

Medication 200Miscellaneous 600

TOTAL 5000

(ii) Hence, complete Table 2 belowItem Average

Monthly

Expenditure forthe year 2012 as base year ( RM)

AverageMonthly

Expenditure forthe year2013(RM)



700 500

Clothing 100 100

Education 500 500Recreation 500 200Utilities

(Water/Electricity/Telephone)400 300


TOTAL 5000 3600

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

Item Price indices for theyear 2013 based on

year 2012

Weightage

Food 100.00 19Accommodation(Rental/ Loan)

38.46 14


71.40 14

Clothing 100.00 3

Education 100.00 14Recreation 40.00 6




75.00 8

Medication 150.00 8Miscellaneous 83.30 14

TOTAL 758.16 100

Formula to calculate price index:

I =index numberQ1 = quantity at specific timeQ0 = quantity at base time

(II) Hence, calculate the composite index for the average monthlyexpenditure in the year 2013 based on year 2012.

Formula to calculate composite index:

∑∑

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

Based on my findings, I found out that the average monthly expenses in year2012 are higher than the current year, 2013. We spent RM1300 inaccommodation in year 2012 compared to RM 500 in year 2013. This is

because of the different prices of land in two different locations. Transportationfee decreases from RM 700 to RM 500 due to shorter distance from new school.

Other fees remain constant due to reduce in quantity but increase in quality.



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 byinstalment.

Table 4(a) shows the prices of televisions by cash payments 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. Brand Size of

Television( Inches)

Price(RM) MeanPrice(RM)

StandardDeviation

(RM)HUP LEE

SHOPSENGHENG

JIT SINSHOP

AB 24 899 1000 900 933 47.3832 1199 1300 1500 1333 125.0840 1399 1500 1600 1500 75.72

EF 24 999 1100 1300 1133 125.0832 1499 1700 1600 1600 75.2840 2199 1900 2000 2033 124.28

Table 4(a)

Brand Size ofTelevision( Inches)

Price(RM) MeanPrice(RM)

StandardDeviation

(RM)HUP LEE

SHOPSENGHENG

JIT SINSHOP

AB 24 1099 1250 1000 1116 106.3532 1399 1550 1600 1516 91.1640 1599 1750 1700 1683 62.81

EF 24 1199 1350 1400 1316 90.4332 1699 1950 1700 1783 118.0940 2399 2150 2100 2216 136.30

Table 4(b)



(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.

I will buy a 24 inch EF television. This is because it fits the size of my furniture

exactly. I choose this brand although it is more expensive than brand AB because it has a history of good serviceability rate and as such very reliable. Ichoose to buy it at Hup Lee Shop because it offers the lowest price compared toother shops. It also offers longer warranty than the other two shops.

(c)The Ministry of Domestic Trade and Consumer Affairs wishes to present theFair Price Shop Award for one of the above shops. If you are one of the panelsfor this award, determine the shop that deserves the award. Do you consider thevalue of the mean and the value of standard deviation in making your decision?Give your justifications.

If I am one of the panels for this award, I would choose Hup Lee Shop as theaward winner. This is because the mean price of all types of television for both

brands is the lowest compared to the other two shops. Standard deviation of allthe televisions in this shop is also comparatively low. This shows that Hup LeeShop has the cheapest televisions in town. It is therefore affordable by anyonewho would like to own a television plus the price are quite reasonable.



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 instalment}

Show the average monthly expenditure that you have modified in a table.

Item Average MonthlyExpenditure

(RM)

Modified Expenditure(RM)



500 500

Clothing 100 0Education 500 500Recreation 200 0


300 300


Television - 999TOTAL 3600 3600

(b) Assuming you have just started working with a monthly salary of RM2500.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 contribution to your parents.

Item Average Monthly Expenditure(RM)Food 350

Accommodation (Rental/ Loan) 300Transportation

(Petrol/Loan/Bus fare etc)200

Clothing 50Education 300

Recreation 50Utilities (Water/Electricity/Telephone) 100



Medication 200Savings 250Parents 700

Miscellaneous 300

TOTAL 2500



Further Exploration

Index numbers are being used in many different daily situations, for example air pollution index, stock market index, gold index and property index.

Air Pollution Index

Air pollution is the introduction of chemicals, particulate matter, or biologicalmaterials that cause harm or discomfort to humans or other living organisms, ordamages the natural environment into the atmosphere.

The atmosphere is a complex dynamic natural gaseous system that is essentialto support life on planet Earth. Stratospheric ozone depletion due to air

pollution has long been recognized as a threat to human health as well as to theEarth's ecosystems.

The Air Quality Index (AQI ) (also known as the Air Pollution Index(API ) orPollutant Standard Index (PSI ) is a number used by government agencies tocharacterize the quality of the air at a given location. As the AQI increases, anincreasingly large percentage of the population is likely to experienceincreasingly severe adverse health effects. To compute the AQI requires an air

pollutant concentration from a monitor or model. The function used to convertfrom air pollutant concentration to AQI varies by pollutant, and is different indifferent countries. Air quality index values are divided into ranges, and eachrange is assigned a descriptor and a color code. Standardized public healthadvisories are associated with each AQI range. An agency might also encouragemembers of the public to take public transportation or work from home whenAQI levels are high.

Limitations of AQI

Most air contaminants do not have an associated AQI. Many countries monitorground-level ozone, particulates, sulphur dioxide, carbon monoxide andnitrogen dioxide and calculate air quality indices for these pollutants.

Causes of poor air quality

The AQI can worsen (go up) due to lack of dilution of air emissions by fresh air.Stagnant air, often caused by an anticyclone or temperature inversion, or otherlack of winds lets air pollution remain in a local area.



Malaysia

The air quality in Malaysia is reported as the API or Air Pollution Index. Fourof the index's pollutant components (i.e., carbon monoxide, ozone, nitrogendioxide and sulfur dioxide) are reported in PM10 particulate matter is reportedin microgram/m3.Unlike the American AQI, the index number can exceed 500. Above 500, astate of emergency is declared in the reporting area. Usually, this means thatnon-essential government services are suspended, and all ports in the affectedarea closed. There may also be a prohibition on private sector commercial andindustrial activities in the reporting area excluding the food sector.



Stock Market Index

A stock market index is a method of measuring a section of the stock market.

Many indices are cited by news or financial services firms and are used as benchmarks, to measure the performance of portfolios such as mutual funds.



Types of indices

Stock market indices may be classed in many ways. A 'world' or 'global' stockmarket index includes (typically large) companies without regard for where theyare domiciled or traded. Two examples are MSCI World and S&P Global 100.

A national index represents the performance of the stock market of a given nationand by proxy, reflects investor sentiment on the state of its economy. The mostregularly quoted market indices are national indices composed of the stocks oflarge companies listed on a nation's largest stock exchanges, such as theAmerican S&P 500, the Japanese Nikkei 225, and the British FTSE100.

The concept may be extended well beyond an exchange. The Dow Jones TotalStock Market Index, as its name implies, represents the stocks of nearly every

publicly traded company in the United States, including all U.S. stocks tradedon the New York Stock Exchange (but not ADR s) and most traded on the

NASDAQ and American Stock Exchange. Russell Investment Group added tothe family of indices by launching the Russell Global Index.

More specialized indices exist tracking the performance of specific sectors ofthe market. The Morgan Stanley Biotech Index, for example, consists of 36American firms in the biotechnology industry. Other indices may trackcompanies of a certain size, a certain type of management, or even morespecialized criteria one index published by Linux Weekly News tracks stocks ofcompanies that sell products and services based on the Linux operatingenvironment.

Uses and importance of air pollution index and stock market index

As everyone can see, the air pollution index is use by the government to

measure the air quality index and to detect any pollutants in our countr y’s air.This is to ensure the air is clean and safe for us to inhale. Besides that, an earlywarning can be given to us if the air pollution is too high for us to get out of ourhomes. This warning is given based upon readings and interpretations of the air

pollution index.

As for the stock market index, it is mainly for the business entrepreneurs. Thistype of index is used to determine the outcome of a stock market and also theconclusion of a stock market. The stock market index is important because acountry’ s economical state sometimes depend on it.



Conclusion

After doing research, answering questions, drawing graphs and some problemsolving, I saw that the usage of index number is important in daily life. It is not

just widely used in markets but also in interpreting the condition of thesurrounding like the air or the water. Especially in conducting an air-pollutionsurvey. In conclusion, statistics is a daily life necessity. Without it, surveyscan’ t be conducted, the stock market can’ t be interpret and many more. So, weshould be thankful of the people who contribute in the idea of statistics.

REFLECTION

What have you learnt while conducting the project? What moral values did you practice? Represent your feelings or opinions creatively through the usage ofsymbols, drawings or lyrics in a song or a poem.

I have learnt that additional mathematics is a very interesting subject and that itis used frequently in our daily lives without us realising it. It can also help usimprove the quality of our daily life indirectly. While doing this project, I hadthe chance to practice managing my time so as to pass up my project on time. Itteaches me to be punctual and it also teaches me to be a patient person.

additional mathematics project (2013)(malaysia)

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