Add Math My Project

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ADDITIONAL MATHEMATICS PROJECT

WORK 4/2010

CURRICULUM DEVELOPMENT DIVISION

MINISTRY OF EDUCATION MALAYSIA

PROJECT WORK 4 :

MARA JUNIOR SCIENCE

COLLEGE

BALIK PULAU

NAME : DESHALENEY A/P LOGANATHAN

NO.IC : 930819-07-5846

CLASS : 5A

TEACHERS NAME : Ms.NOORAINI

STATISTICS


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INTRODUCTION

The Curriculum Development Division,Ministry of Education has prepared four tasks for usthis year.We,the Form 5 student have to choose andcomplete only ONE task based on our area ofinterest.This project is been done by s orindividually,and each of us are expected to submitan individually written report before the due date.Bydoing this project,we are actually gaining a lot of

valuable knowledge in daily life.This is also help toapply the strategics to solve our routine and non-routine problems

Experience classroom environments whichare challenging, interesting and henceimprove their thinking skills

Experience classroom environments which

expressing ones mathematicalthinking,reasoning and communication arehighly encouraged and expected

Acquire effective mathematicalcommunication through oral andwriting,and to use the language ofmathematics to express mathematicalideas correctly and smartly

Prepare ourselves for the demand of our


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future undertakings and in workplace Train ourselves not only to be independent

learners but also to collaborate, tocooperate, and to share knowledge in thiscultural environment

Use technology especially the ICT

appropriately and effectively Train ourselves to appreciate the intrinsic

values of mathematics and to become morecreative and innovative

Realize the importance and the importantof mathematics

APPR ECIA TION .

Thank you foremost to myparents,Mr.Loganathan and Mrs.Gavairi

for giving the will,support and biggestencouragement to do my additionalmathehatics project. Secondly, I wouldlike to thank my homeroom mother forgiving the heartless support to finish myAdditional Mathematics Project

Work.Besides that,I also like to said aappreciation to my beloved AdditionalMathematics teacher, Pn Nooraini for giveme the guide and giving useful andimportant information tocomplete this project work.Last but notleast,a special thanks to all my friends for

their help and cooperation in searching


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for information and completing thisAdditional Mathematics projectwork.Thank you also to the one whoinvolved in helping me indirectly to finishthis project before the due date.

HISTORY oF STATISTICS

By the 18th century, the term "statistics" designed tothe systematic collection of demographic and economicdata by states. In the early 19th century, the meaning of"statistics" broadened, thenincluding the discipline concerned with the collection,summary,and analysis of data. Today statistics is widely employed ingovernment, business, and all the sciences.Electroniccomputers have expedited statistical computation, andhave allowed statisticians to develop "computer-intensive"methods.

The term "mathematical statistics" designates themathematical


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theories of probability and statistical inference, which areusedin statistical practice. The relation between statistics andprobability theory developed rather late, however. In the19thcentury, statistics increasingly used probability theory,whose

initial results were found in the17th and 18th centuries,particularlyin the analysis ofgames of chance (gambling). By 1800,astronomy used probability models and statistical theories,particularly the method of least squares, which wasinventedby Legendre and Gauss. Early probability theory andstatistics wassystematized and extended by Laplace; following Laplace,

probability and statistics have been in continualdevelopment.In the 19th century, social scientists used statistical

reasoning and probability models to advance the newsciences ofexperimentalpsychology and sociology; physical scientists usedstatisticalreasoning and probability models to advance the newsciencesof thermodynamics and statistical mechanics. Thedevelopment ofstatistical reasoning was closely associated with thedevelopmentofinductive logic and the scientific method.

Statistics is not a field of mathematics but anautonomous mathematical science, like computer scienceor operations research.Unlike mathematics, statistics had itsorigins in public administration and maintains a specialconcern with demography and economics. Being concerned

with the scientific method and inductive logic, statisticaltheory has close association with the philosophy of science;with its emphasis on learning from data and making bestpredictions, statistics has great overlap with the decisionscience and microeconomics.

With its concerns with data, statistics has overlapwith information science and computer science.It hasbrought a lot of benefits to the humankind


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MODERN STATISTICS

During the 20th century, the creation ofprecise instruments for agricultural research, public

health concerns(epidemiology, biostatistics, etc.), industrial qualitycontrol,and economic and social purposes (unemploymentrate, econometry, etc.) necessitated substantialadvances in statistical practices.

Today the use of statistics has broadened far

beyond its origins.Individuals and organizations usestatistics to understand data and make informeddecisions throughout the natural and socialsciences, medicine, business, and other areas.

Statistics is generally regarded not as asubfield of mathematics but rather as a distinct,albeit allied, field.Many universities maintain

separate mathematics and statistics departments.Statistics is also taught in departments as diverse aspsychology, education, and public health.


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After the survey....,a) Collection of pictures

b) Record the items and their prices

systematically as in Table1.Since items maybe differently packed,besure to use consistent measurements foreach item selected so that comparison can be

done easily and accurately.


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ANSWER :


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TABLE 1

CATEGOR

YITEM

PRICE(RM)

PASAR

AYA

TESCO

PASAR

AYA

ECONS

AVE

PASARA

YA

MEGAM

ALL

FOOD 1.SELF-RAISING

FLOUR (1000 g)4.00 3.70 3.60

2.SUGAR (1000g) 2.00 1.90 1.80

3.BUTTER (250g) 4.70 4.50 4.30

4.EGGS (GRADEA) 1 DOZEN

5.90 5.50 5.00

TOTAL PRICE 16.60 15.60 14.70

DETERGEN

T

1.LUX ( 3 BARS) 3.20 3.00 2.80

2.AXION (DISHWASHER)-1000ml

4.29 3.90 3.20

3.CLOTHESDETERGENT (3KG)

18.90 17.00 16.50

4.AJAX(TOILETCLEANER)(500ml)

5.50 5.50 5.50

TOTAL PRICE 31.89 29.40 28.00

STATIONERY

1.HIGHLIGHTER 1.50 1.30 1.00

2.PENCIL (EXAMGRADE) 1DOZEN

5.00 4.80 4.50

3.PEN(KILOMETRICO)

1.30 1.20 1.00

4.ERASER(STABILO)

1.30 1.20 1.10

TOTAL PRICE 9.10 8.50 7.60

GRAND TOTAL 57.59 53.50 50.30


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c)Create at least two suitable graphicalrepresentation

to compare and contrast the prices ofthe items chosen.

FOOD

FlourSugarButterEggs

TESCO ECONSAVE MEGAMALL

7

6

5

4

3

4

2

1

0


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DETERGENT

Soap (3 bar)

Liquiddishwasher(1000ml)

Toiletcleaner(500ml)

2

1

1

1

1

1

TESCO ECONSAVE MEGAMALL


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STATIONERY


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PART 1 (C)

d)Based on the graphical representation

that you have

1

HIGHLIGTERPENCIL

PEN

6

2

3

4

5

0TESCO MEGAMALLECONSAVE


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constructed in Part 1(c),interpret,discuss and draw

conclusions. Comments on yourfindings.

ANSWER :

PART 1 (D)

TESCO

ECONSA

VE

GRAND

6

5

5

5

5

5

4

4


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Based on the graphical representations that Ihave constructed in Part 1(c), it is shown that thereare large and small differences among the prices ofitems in each category between the shops.In thefood category, the smallest price

difference are of those of sugar, while the highest isthe price of eggs.Besides food, detergent also showsa large price difference between its items.For them,is the price of liquid dishwasher and clothesdetergent.

On the other hand, stationery items doesnthave any obvious price difference. The graph alsoshow that most of the items that are high priced

comes from the PASARAYA TESCO, while the lowestprice items come from the PASARAYAMEGAMALL.The graph 1(d) had show the conclusionofthe difference among the shops based upon theshops grand total.

Question (e) :Identify an item that has a large price

differenceamong the shops. Calculate the mean andstandard deviationof that particular item. Hence, suggest anddiscuss possiblereasons for the price difference.


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Answer :

Clothes d etergent :

MEAN : 18.9 + 17

+ 16.5

3= 17.47

STANDARDDEVIATION

= (2)/N ( x )2


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18.9 +17 + 16.5

_(17.47)2

3= 0.97

The large price difference of clothes

detergent among the shops maybe because ofthe standard of the shop.A high standard shopor supermarket, theitems sold intend to be much more expensivethan a regular shop or supermarket.Also, theprice difference of the items may also due tothe economic level in our country right

now.So, in order to achieve more profit,someintend to sell in higher prices.


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Every year SMK Indah organises a carnivalto raise funds for the school. This year the

school plans to install air conditioners inthe school library. Last year, during thecarnival, your class made and sold

butter cakes. Because of the popularityof butter

cakes,your has decided to carry outsome project

for this years carnival.

Question (a) :Suggest a shop from Part 1 which you wouldgo to

purchase the ingredients for the buttercakes.State anddiscuss your reasons for purchasing from theshop yousuggested.

Answer:


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I will choose the PASARAYA MEGAMALL. This isbecause the total price of the ingredients fromthis shop is the lowest from the three

shops.This would help to gain more profitbecause we did not need to invest a lot inselling.

Question (b) :

Complete Table 2 with the prices of the itemsfound in the shop/supermarket that you havechosen.


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TABLE 2

Question (i)

Calculate the price index for each of theingredients in Table 2 for theyear 2010 based

on the year 2009.

INGREDIENT

QUANTITYPER CAKE

PRICE INTHE YEAR2009(RM)

PRICE INTHE YEAR2010(RM)

Self-RaisingFlour

250g 0.90 0.90

Sugar 200g 0.35 0.36

Butter 250g 3.30 4.30

Eggs (GradeA)

5 eggs(300g)

1.25 2.10


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SOLUTION :

A] Self-raising flour = 0.9 0.9 100 = 100.00

B] Sugar = 0.36 0.35 100 = 102.86

C] Butter = 4.30 3.30 100 = 130.30

D] Eggs(Grade A) = 2.10 1.25 100 = 168.00

INGREDIENT

QUANTITY PERCAKE

PRICEIN THEYEAR2009(R

M)

PRICEIN THEYEAR2010(R

M)

PRICE INDEXFOR THE

YEAR2010BASED ON THEYEAR 2009(I)

Self-RaisingFlour

250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86

Butter 250g 3.30 4.30 130.30

Eggs

(Grade A)

5 eggs

(300g)

1.25 2.10 168


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(ii) Calculate the composite index for making abutter cake in the year 2010 based on the year2009.Discuss how you obtained your answer.

= To calculate the compositeindex,weightageis needed

( ) WEIGHT

TOTAL WEIGHT

INGREDIENT WEIGHTAGE (W)

Self-Raising Flour250/ 1000 = 1/4

Sugar 200 / 1000 = 1/5

Butter 250 /1000 = 1 /4

Eggs (Grade A) 300 / 1000 = 3 /10


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Thus,the suitable price for the

butter cake for the year 2010 is

RM19.30.The increase in price is

also suitable due to the economic

crisis having by the country and

the prices of some ingridients hadincrease in price,so I think

RM19.30 would be a suitable

prices .

(c)

(i) Find out from reliable source how todetermine suitable capacity of airconditioner to be installed based on thevolume/size of a room.

Answer:

For common usage, air conditioner israted according to horse power(1HP), which is approximately 700Wto 1000W of electrical power. It issuitable for a room size 1000ftwhich is around 27m of volume.


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(ii) Work in group to estimate the volume ofyour school library.Explain how you arriveat your answer.Hence,determine thenumber of air conditioners with theappropriate capacity required for yourlibrary.

Answer:

By using a measuring tape,the dimension

for the library is:

Height = 3.6mWidth = 9.17mLength = 20.12m

Volume of the room = 3.8 x 9.19 x 20.14

=HEIGHT 3.8 m

= 9.1WIDTH 9 m

=LENGTH 20.14 m


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= RM 703.33 m3

1 unit of air conditioner is for 27m

For 703.33 m3 = 703.33

27

= 26.0

That means our school library needs 26unit of air conditioner.

(iii) If your class intends to sponsor one airconditioner for the school library, howmany butter cakes must you sell in order tobuy the air conditioner

Answer:

1 unit of 1HP air conditioner = RM 800Cost for a cake = 0.9 + 0.36 +4.3 + 2.1

= RM 7.66


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Selling price = RM19.30Profit = 19.30 7.66

= RM 11.64

Number of cakes to buy 1 unit of air conditioner =

Number of cakes = 69 cakes

Question

As a committee member for the carnival, you arerequired to prepare an estimated budget toorganize this years carnival. The committee hasto take into the consideration the increase in

expenditure from the previous year due toinflation. The price of food, transportation andtents has increased by 15%. The cost of games,prizes and decorations remains the same,whereas the cost of miscellaneous items hasincrease by 30%.

= 800

11.64

= 68.73


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(a) Complete Table 3 based on the information givenabove

Answer:

EXPENDITUR

E

AMOUNT

IN 2009

(RM)

AMOUNT

IN 2010

(RM)

FOOD 1200.00 1340.00

GAMES 500.00 600.00

TRANSPORTATION

300.00 345.00

DECORATIONS 200.00 250.00

PRIZES 600.00 600.00

TENTS 800.00 900.00MISCELLANEOUS

400.00 550.00

Table 3

(b) Calculate the composite index for theestimated budget of the carnival in the year2010 based on the year 2009. Comment onyour answer.


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Answer:

EXPENDITU

RE

AMOUN

T IN

2009

(RM)

AMOU

NT IN

2010

(RM)

PRIC

E

INDE

X, I

I=

P1P0

X

100%

WEIGHT

AGE, W

FOOD 1200.00 1340.00 112 10

GAMES 500.00 600.00 120 5

TRANSPORT

ATION

300.00 345.00 115 4

DECORATIO

NS

200.00 250.00 125 2

PRIZES 600.00 600.00 100 7

TENTS 800.00 900.00 113 8

MISCELLAN

EOUS

400.00 550.00 138 3


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COMPOSITE INDEX

=Ii wi

wi

= 112(10) + 120(5) + 115(4) + 125(2) + 100(7) + 113(8)

+ 138(3)

10 + 5 + 4 +2 +7 + 8 + 3

= 4448 = 114.0539

The total price for the year 2010increase by 11. 40 5%.This is becaus esome price in the year 2009 increased

in the year 2010.


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(a)The change in the composite index for theestimate budget for the carnival from theyear 2009 to the year 2010 is the same asthe change from the year 2010 to the year2011. Determine the composite index of thebudget for the year 2011 based on the year2009.

Answer:

Composite index for the year 2009 to the year2010

= 114.05Composite index for the year 2010 to the year2011

= 114.05

I20112009 X 100 = I20102009 X I20112009

I20112009 = 114.05 X 114.05 X 1100

I20112009 = 130.07


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FURTHER EXPLORATION

Index numbers are being used in manydifferent daily situations, for example airpollution index, stock market index, goldindex and property index.Obtain informationfrom the internet or other reliable sources

on the importance of two different types ofindex number of your choice. Elaborate theuse and the importance of these indexnumbers in daily life.

AIR POLLUTION INDEX

Air pollution is the introduction of chemicals,particulate matter,or biological materials thatcause harm or discomfort to humans or otherliving organisms, or damages the naturalenvironment into the atmosphere.

The atmosphere is a complex dynamic naturalgaseous system that is essential to support life onplanet Earth. Stratospheric ozone depletion due toair pollution has long been recognized as a threat tohuman health as well as to the Earth's ecosystems.

The Air Quality Index (AQI) (also known as theAir Pollution Index (API) or Pollutant


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Standard Index (PSI) is a number used bygovernment agencies to characterize the qualityof the air at a given location. As the AQIincreases, an increasingly large percentage ofthe population is likely to experienceincreasingly severe adversehealth effects. To compute the AQI requiresan air pollutant concentration from a monitoror model. The function used to convert fromair pollutant concentration to AQI varies bypollutant, and isdifferent in different countries. Air quality indexvalues are divided into ranges, and each range isassigned a descriptor and a color code.

Standardized public health advisories areassociated with each AQI range. An agency mightalso encourage members of the public to takepublic transportation or work from home when AQIlevels are high.

Limitations of theAQI

Most air contaminants do not have an associatedAQI. Many countries monitor ground-level ozone,

particulates, sulphur dioxide, carbon monoxide and

nitrogen 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 byan anticyclone or temperature inversion, or otherlack of winds lets air pollution remain in a local area.


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Indices by location

South Korea

The Ministry of Environment of South Korea uses theComprehensice Air-quality Index (CAI) to describethe ambient air quality based on health risk of airpollution. The index aims to help the public easilyunderstand air quality level and protect the health ofpeople from air pollution. - The CAI has values of 0through 500, which are divided into six categories.

The higher the CAI value, the greater the level ofair pollution. - Of values of the five air pollutants,the highest is the CAI value.

Malaysia

The air quality in Malaysia is reported as the API or

Air Pollution Index. Four of the index's pollutantcomponents (i.e., carbon monoxide, ozone,nitrogen dioxide and sulfur dioxide) are reportedin PM10 particulate matter is reported ing/m.Unlike the American AQI, the index numbercan exceed 500. Above 500, a state of emergencyis declared in the reporting area. Usually, this

means that non-essential government services aresuspended, andall ports in the affected area closed. There may alsobe a prohibition on private sector commercial andindustrial activities in the reporting area excludingthe food sector.


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STOCK MARKET INDEX

A comparison of tree major U.S. stock indices:the NASDAQ Composite, Dow Jones IndustrialAverage, andS&P 500. All three have the sameheight at March 2007. Notice the large dot comspike on the NASDAQ, a result of the largenumber of tech. companies on that index.

A stock market index is a method of measuring asection of the stock market. Many indices are citedby news or financial services firms and are used asbenchmarks, to measure the performance ofportfolios such as mutual funds.

Types of

indices

Stock market indices may be classed in manyways. A 'world' or 'global' stock market indexincludes (typically large) companies withoutregard for where they are domiciled or traded.

Two examples are MSCI World and S&P Global

100.

A national index represents the performance of thestock market of a given nationand by proxy,reflects investor sentiment on the state of itseconomy. The most regularly quoted market indicesare national indices composed of the stocks of large

companies listed on a nation's largest stock


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exchanges, such as the American S&P 500, theJapanese Nikkei 225, and the British FTSE 100.

The concept may be extended well beyond anexchange. The Dow Jones Total Stock Market

Index, as its name implies, represents the stocksof nearly every publicly traded company in theUnited States, including all U.S. stocks traded onthe New York Stock Exchange (but not ADRs) andmost traded on the NASDAQ and American StockExchange. Russell Investment Group added to thefamily of indices by launching the Russell Global

Index.


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More specialised indices exist tracking theperformance of specific sectors of the market. TheMorgan Stanley Biotech Index, for example, consistsof 36 American firms in the biotechnology industry.Other indices may track companies of a certain size,a certain type of management, or even morespecialized criteria one index published by LinuxWeekly News tracks stocks of companies that sellproducts and services based on the Linux operatingenvironment.

Index versions

Some indices, such as the S&P 500, have multiple

versions.[1] These versions can differ based on howthe index components are weighted and on howdividends are accounted for. For example, there arethree versions of the S&P 500 index: price return,which only considers the price of the components,total return, which accounts for dividendreinvestment, and net total return, which accounts fordividend reinvestment after the deduction of awithholding tax. As another example, the Wilshire4500 and Wilshire 5000 indices have five versionseach: full capitalization total return, full capitalizationprice, float-adjusted total return, float-adjusted price,and equal weight. The difference between the fullcapitalization, float-adjusted, and equal weightversions is in how index components are weighted.


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USES AND IMPORTANCE OF AIRPOLLUTION INDEX AND STOCKMARKET INDEX

As everyone can see,the air pollution index is use bythe government to measure the quality of air indexand to detect any pollutants in our countrys air.Thisis to ensure the air is clean and safe for us tiinhale.Besides that,an early warning can be given tous if the air pollution is too high for us to get out ofour homes.This warning is given based upon readingsand unterpretations of the air index.

As for the stock market index, it is mainly for thebusiness entrepreneurs. This type of index is used todetermine the outcome of a stock market and also theconclusion of a stock market. The stock market indexis important because a countrys economical statesometimes depend on it.


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CONCLUSION

After doing research,answering questions,drawinggraphs and some problem solving, I saw that theusage of statistics is important in daily life.It is not just

widely used in markets but also in interpreting thecondition of the surrounding like the air or thewater.Especially in conducting an air-pollutionsurvey.In conclusion,statistics is a daily lifenessecities.Without it,surveys cant be conducted,thestock market cant be interpret and many more.So,weshould be thankful of the people who contribute in theidea of statistics.


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REFLECTION

After spending countless hours,days andnight to finish this project and alsosacrificing my playingtime,facebook,laptop,there are severalthings that I can say...

Additional Mathematics...From the day I am form 4From the day I was able to understand u...From the day I start learning the miracle...And...From the day I heard the name people fearmost......


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I always thought that you will be mygreatest obstacle and rival in excelling in

my life...But after countless of hours...Countless of days...Countless of nights...

After sacrificing my precious time just for

you...Sacrificing my playing time...Sacrificing my laptop...Sacrificing my Facebook...Sacrificing my Internet...Sacrifing my arts...Sacrificing my boyfriend...I realized something really important inyou...

I really love you...You are my real friend...You my life partner...

You are my best boyfriend ever...I LOVE U ADDITIONAL MATHEMATICS...


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