addmath sample 1

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Statistics In Our Daily LifePROJECT WORK FOR ADDITIONAL

MATHEMATHICS 2010

Nama:Mohammad.Irwandy bin Mohammad.Jali

Guru Pembimbing: Puan Rosmeela

Kolej Datu Patinggi Abang Haji Abdillah


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IntroductionWe students taking Additional Mathematics are required to carry out

a project work while we are in Form 5.This year the CurriculumDevelopment Division, Ministry of Education has prepared four tasksfor us.We are to choose and complete only ONE task based on ourarea of interest..Upon completion of the Additional MathematicsProject Work,we are to gain valuable experiences and able to:

y Apply and adapt a variety of problem solving strategies tosolve routine and non-routine problems;

y Experience classroom environments which are challenging,interesting and meaningful and hence improve their thinkingskills.

y Experience classroom environments where knowledge andskills are applied in meaningful ways in solving real-lifeproblems

y Experience classroom environments where expressing onesmathematical thinking,reasoning and communication arehighly encouraged and expected

y Experience classroom environments that stimulates and

enhances effective learning.y Acquire effective mathematical communication through oral

and writing,and to use the language of mathematics to expressmathematical ideas correctly and precisely

y Enhance acquisition of mathematical knowledge and skillsthrough problem-solving in ways that increase interest andconfidence

y Prepare ourselves for the demand of our future undertakingsand in workplace

y Realise that mathematics is an important and powerful tool insolving real-life problems and hence develop positive attitudetowards mathematics.


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y Train ourselves not only to be independent learners but also tocollaborate, to cooperate, and to share knowledge in anengaging and healthy environment

y Use technology especially the ICT appropriately andeffectively

y

Train ourselves to appreciate the intrinsic values ofmathematics and to become more creative and innovative

y Realize the importance and the beauty of mathematics

We are expected to submit the project work within three weeksfrom the first day the task is being administered to us.Failure tosubmit the written report will result in us not receiving certificate.


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Appreciation

Alhamdullilah,thank you to Allah for giving the will to do my additional

mathehatics project.Secondly, I would like to thank the principle of Kolej Datu

Patinggi Abang Haji Abdillah, Puan Johara Binti Zen for giving the permission to

do my Additional Mathematics Project Work. I also like to thank my Additional

Mathematics teacher, Madam Rosmeela for the guide and giving useful and

important information for me to complete this project work. Besides that, Iwould like to thank my parents for their support and encouragement. Lastly, a

special thanks to all my friends for their help and cooperation in searching for

information and completing this project work.


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History of statistic

By the 18th century, the term "statistics" designated the systematiccollection of demographic and economic data by states. In the early 19thcentury, the meaning of "statistics" broadened, then including the disciplineconcerned with the collection, summary, and analysis of data. Today statistics iswidely employed in government, business, and all the sciences.Electronic computers have expedited statistical computation, and have allowedstatisticians to develop "computer-intensive" methods.

The term "mathematical statistics" designates the mathematical theoriesof probability and statistical inference, which are used in statistical practice. Therelation between statistics and probability theory developed rather late,however. In the 19th century, statistics increasingly used probability theory,whose initial results were found in the17th and 18th centuries, particularly in

the analysis of games of chance (gambling). By 1800, astronomy usedprobability models and statistical theories, particularly the method of leastsquares, which was invented by Legendre and Gauss. Early probability theoryand statistics was systematized and extended by Laplace; following Laplace,probability and statistics have been in continual development. In the 19thcentury, social scientists used statistical reasoning and probability models toadvance the new sciences of experimental psychology and sociology; physicalscientists used statistical reasoning and probability models to advance the newsciences of thermodynamics and statistical mechanics. The development of

statistical reasoning was closely associated with the development of inductivelogic and the scientific method.

Statistics is not a field of mathematics but an autonomous mathematical science,like computer science or operations research. Unlike mathematics, statistics hadits origins in public administration and maintains a special concernwith demography and economics. Being concerned with the scientificmethod and inductive logic, statistical theory has close association withthe philosophy of science; with its emphasis on learning from data and makingbest predictions, statistics has great overlap with the decision

science and microeconomics. With its concerns with data, statistics has overlapwith information science and computer science.


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Statistics today

During the 20th century, the creation of precise instruments for agriculturalresearch, public health concerns (epidemiology, biostatistics, etc.),industrial quality control, and economic and social purposes(unemployment rate, econometry, etc.) necessitated substantial advances instatistical practices.

Today the use of statistics has broadened far beyond its origins. Individualsand organizations use statistics to understand data and make informeddecisions throughout the natural and social sciences, medicine, business,and other areas.

Statistics is generally regarded not as a subfield of mathematics but ratheras a distinct, albeit allied, field. Many universities maintain separatemathematics and statistics departments. Statistics is also taught indepartments as diverse as psychology, education, and public health.


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Part 1

The prices of goods sold in shops vary from one shop toanother.Shoppers tend to buy goods which are not only reasonablypriced but also give value for their money.

You are required to carry out a survey on four different items basedon the following categories i.e. food, detergent and stationery.Thesurvey should be done in three different shops.

a)Collect pictures,newspaper cuttings or photos on items that youhave chosen.Design a collage to illustrate the chosen items

Answer:


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Food


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Question

(b) Record the items and their prices systematically as inTable 1.Since items maybe differently packed,be sure to use

consistent measurements for each item selected so thatcomparison can be done easily and accurately.

Answer:

Category Item Price(RM)Boulevard Everrise Discount

store

Food1.Self-RaisingFlour(1000g)

4.00 3.70 3.60

2.Sugar(1000g) 2.00 1.90 1.803.Butter(250g) 4.70 4.50 4.304.Eggs(Grade A)1 dozen

5.90 5.50 5.00

Total Price 16.60 15.60 14.70

Detergent

1.Soap(3 bars) 3.20 3.00 2.80

2.Liquiddishwasher(1000ml) 4.29 3.90 3.20

3.Clothesdetergent(3kg)

18.90 17.00 16.50

4.Toiletcleaner(500ml)

5.50 5.50 5.50

Total Price 31.89 29.40 28.00

Stationery1.Sharpener 1.50 1.30 1.002.Pencil

(2B-1 dozen)

5.00 4.80 4.50

3.Pen 1.30 1.20 1.004.Eraser 1.30 1.20 1.10

Total Price 9.10 8.50 7.60Grand Total 57.59 53.50 50.30


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Question

(c) Create at least two suitable graphical representations (theuse of ICT is encouraged) to compare and contrast the price ofthe items chosen.

Answer:

1)

0

1

2

3

4

5

6

7

Boulevard Everrise Discount store

Self-raising flour

Sugar

Butter

Eggs(Grade A)


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2)

0

2

4

6

8

10

12

14

16

18

20


Soa

(3 ar)

Liquid dishwasher(1000ml)

Toilet cleaner(500ml)

Clothes detergent(3 kg)


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3)

0

1

2

3

4

5

6


Sharpener

encil 2B(1 Dozen)

en

Eraser


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Question

(d) Based on the graphical representation that youhave constructed in Part 1(c), interpret,discuss and drawconclusions. Comments on your findings.

Answer:

Based on the graphical representations that I haveconstructed in Part 1(c), it is shown that there are largeand small differences among the prices of items in each

category between the shops.In the food category, thesmallest price difference are of those of sugar, while thehighest is the price of eggs. Besides food, detergent alsoshows a large price difference between its items.Among them is the price of liquid dishwasher andclothes detergent. On the other hand,stationery items

doesnt have any obvious price difference. The graphalso show that most of the items that are high pricedcomes from the Boulevard Supermarket, while thelowest price items come from the Discount Store.Thegraph 1(d) will show the conclusion of the differenceamong the shops based upon the shops grand total.


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Graph 1(d)

46

48

50

52

54

56

58

60

Grand total

Boulevard

Everrise

Discount store


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Question

(e) Identify an item that has a large price differenceamong the shops. Calculate the mean and standarddeviation of that particular item. Hence, suggest and

discuss possible reasons for the price difference.Answer:

Liquid dishwasher:

Mean=

=17.47

Standard deviation

= ()/N ( )

=

- (17.47)

=0.97The large price difference of clothes detergent amongthe shops maybe because of the standard of the shop.Ahigh standard shop or supermarket, the items soldintend to be much more expensive than a regular shopor supermarket.Also, the price difference of the items

may also due to the quality of the item present. A betterquality means a higher price.


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Part 2Every year SMK Indah organises a carnival to raise funds for theschool. This year the school plans to install air conditioners in theschool library. Last year, during the carnival, your class made andsold butter cakes. Because of the popularity of the buttercakes,your class has decided to carry out the same project for thisyears carnival.

Question

(a) Suggest a shop from Part 1 which you would go topurchase the ingredients for the butter cakes.State anddiscuss your reasons for purchasing from the shop you

suggested.

Answer:

The Discount Store.This is because the total price of theingredients from this shop is the lowest from the three shops.

Question

(b) Complete Table 2 with the prices of the items found inthe shop/supermarket that you have chosen.

Answer:

Ingredient QuantityPer cake

Price in the year2009(RM)

Price in theyear 2010(RM)

Self-raising flour 250g 0.90 0.90Sugar 200g 0.35 0.36Butter 250g 3.30 4.30Eggs(Grade A) 5 eggs (300g) 1.25 2.10


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Question

(i) Calculate the price index for each of the ingredients in Table 2for the year 2010 based on the year 2009

Answer:

1.Self-raising flour

=

2.Sugar

=

3.Butter

=

4.Eggs(Grade A)

=

Ingredient QuantityPer cake

Price in theyear

2009(RM)

Price in theyear

2010(RM)

Price indexfor the year

2010 based onthe year 2009

()Self-raisingflour

250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86

Butter 250g 3.30 4.30 130.30Eggs(GradeA)

5 eggs(300g)

1.25 2.10 168


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Question

(ii) Calculate the composite index for making a buttercake in the year 2010 based on the year 2009. Discusshow you obtained your answers.

Answer:

To calculate the composite index,weightage is needed

(W),

Ingredients Weightage (W)Self-raising flour

Sugar

Butter

Eggs(Grade A)

Composite

index

=128.54


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Question

(iii) In the year 2009,the butter cake was sold at RM15.00each.Suggest a suitable selling price for the butter cake in theyear 2010.Give reasons for your answer.

Answer:On 2009,RM 15.00

On 2010, price=

= =19.30

Thus,the suitable price for the butter cake for the year

2010 is RM19.30.The increase in price is also suitable

because of the rise in the price of the ingredients.


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Question

(c)(i) Find out from reliable sources how to determinesuitable capacity of air conditioner to be installed basedon the volume/size of a room.

Answer:

For common usage,air conditioner is rated according tohorse power (1HP), which is approximately 700W to1000W of electrical power. It is suitable for a room size1000ft which is around 27m of volume.

Question(ii) Work in groups to estimate the volume of yourschool library. Explain how you arrive at your answer.Hence, determine the number of air conditioners withthe appropriate capacity required for your library.

Answer:By using a measuring tape,the dimension for the libraryis:

Height=3.6m

Width=9.17m

Length=20.12mVolume of the room=3.69.1720.12

=664.20m


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1 unit of air conditioner is for 27m

For 664.20m=

=24.6

That means our school library needs 25 unit of airconditioner.

Question

(iii) If your class intends to sponsor one airconditioner for the school library, how many buttercakes must your class sell in order to buy the airconditioner?

Answer:

1 unit of 1HP air conditioner=RM700Cost for a cake =0.9+0.36+4.3+2.1 =7.66

Selling price =RM19.30

Profit =19.30-7.66

=RM11.64Number of cakes to buy 1 unit of air conditioner =

= 60.13 = 60 cakes


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Part 3

As a committee member for the carnival, you arerequired to prepare an estiated budget to organize thisyears carnival. The committee has to take into the

consideration the increase in expenditure from theprevious year due to inflation. The price of food,transportation and tents has increased by 15%. The costof games, prizes and decorations remains the same,whereas the cost of miscellaneous items has increase by30%.

Question,

a)Complete Table 3 based on the information givenabove.

Answer ,

Expenditure Amount in 2009(RM)

Amount in 2010(RM)

Food 1200.00 1380.00Games 500.00 500.00Transportation 300.00 345.00Decorations 200.00 200.00

Prizes 600.00 600.00Tents 800.00 920.00Miscellaneous 400.00 520.00

Table 3


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Question

b)Calculate the composite index for the estimatedbudget of the carnival in the year 2010 based on theyear 2009. Comment on your answer.

Solution.

Expenditure Amountin 2009(RM)

Amountin 2010(RM)

PriceIndex,

I

I=

Weightage,W

Food 1200.00 1380.00 115 12Games 500.00 500.00 100 5Transportation 300.00 345.00 115 3Decorations 200.00 200.00 100 2Prizes 600.00 600.00 100 6

Tents 800.00 920.00 115 8Miscellaneous 400.00 520.00 130 4

Composite Index

=

=

= =111.625


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The total price for the year 2010 increase by 11.625%.This is because some price in the year 2009 increased inthe year 2010.Question.

c)The change in the composite index for the estimate budget for the carnival from the year 2009 to theyear 2010 is the same as the change from the year2010 to the year 2011. Determine the compositeindex of the budget for the year 2011 based on the

year 2009.Solution.

Composite index for the year 2009 to the year 2010

=111.625

Composite index for the year 2010 to the year 2011

=111.625

E

=E

E

E

=111.625111.625

E 124.60


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Further Exploration

Index numbers are being used in many different dailysituations, for example air pollution index, stock marketindex, gold index and property index.

Obtain information from the internet or other reliable sourceson the importance of two different types of index number ofyour choice. Elaborate the use and the importance of theseindex numbers in daily life.


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Indices by location

South Korea

The Ministry of Environment of South Korea uses the ComprehensiceAir-quality Index (CAI) to describe the ambient air quality based onhealth risk of air pollution. The index aims to help the public easily

understand air quality level and protect the health of people from airpollution. - The CAI has values of 0 through 500, which are dividedinto six categories. The higher the CAI value, the greater the level ofair pollution. - Of values of the five air pollutants, the highest is theCAI value.

CAI Description Health Implications

0-50 Good A level that will not impact patients suffering from diseases related to air pollution.

51-100

Moderate A level which may have a meager impact on patients in case of chronic exposure.

101-150

Unhealthy forsensitive groups

A level that may have harmful impacts on patients and members of sensitivegroups.

151-250

UnhealthyA level that may have harmful impacts on patients and members of sensitivegroups (children, aged or weak people), and also cause the general publicunpleasant feelings.

251-350

Very unhealthyA level which may have a serious impact on patients and members of sensitivegroups in case of acute exposure.

351-500

HazardousA level which may need to take emergency measures for patients and members ofsensitive groups and have harmful impacts on the general public.


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Malaysia

The air quality in Malaysia is reported as the API or Air PollutionIndex. Four of the index's pollutant components (i.e., carbonmonoxide, ozone, nitrogen dioxide and sulfur dioxide) are reportedin PM10 particulate matter is reported in g/m.

Unlike the American AQI, the index number can exceed 500. Above500, a state of emergency is declared in the reporting area. Usually,this means that non-essential government services are suspended, andall ports in the affected area closed. There may also be a prohibitionon private sector commercial and industrial activities in the reportingarea excluding the food sector.


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St M t Index

A compari on oft ree major U.S. stockindices:t eNASDAQComposite, Dow Jones Industrial Average, andS&P 500. Allt reehave the same height atMarch 2007. Notice the large dot com spikeon the NASDAQ, a result ofthe large number oftech. companies onthatindex.

A stock market i exis a method of measuring a section ofthe stockmarket. Many indices are cited by news or financial services firmsand are used as benchmarks, to measure the performanceof portfolios such as mutual funds.

Types ofindices

Stock marketindices may be classed in many ways. A 'world' or'global' stock marketindex includes (typically large) companieswithout regard for where they are domiciled ortraded. Two examples

are MSCI World and S&P Global 100.A nationalindex represents the performance ofthe stock market of agiven nationand by proxy, reflects investor sentiment on the state ofits economy. The most regularly quoted marketindices are nationalindices composed ofthe stocks oflarge companies listed on a nation'slargest stock exchanges, such as the American S&P 500, theJapanese Nikkei 225, and the British FTSE 100.

The concept may be extended well beyond an exchange. The Dow

Jones Total StockMarket Index, as its name implies, represents thestocks of nearly every publicly traded company in the United States,including all U.S. stocks traded on the New York StockExchange (but not ADRs) and mosttraded onthe NASDAQ and American Stock Exchange. Russell InvestmentGroup added to the family ofindices by launching the Russell GlobalIndex.


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More specialised indices exist tracking the performance of specificsectors of the market. The Morgan Stanley Biotech Index, forexample, consists of 36 American firms in the biotechnology industry.Other indices may track companies of a certain size, a certain type ofmanagement, or even more specialized criteria one indexpublished by Linux Weekly News tracks stocks of companies that sell

products and services based on the Linux operating environment.

Index versions

Some indices, such as the S&P 500, have multiple versions.[1] Theseversions can differ based on how the index componentsare weighted and on how dividends are accounted for. For example,there are three versions of the S&P 500 index: price return, whichonly considers the price of the components, total return, which

accounts for dividend reinvestment, and net total return, whichaccounts for dividend reinvestment after the deduction of awithholding tax. As another example, the Wilshire 4500 and Wilshire5000 indices have five versions each: full capitalization total return,full capitalization price, float-adjusted total return, float-adjustedprice, and equal weight. The difference between the fullcapitalization, float-adjusted, and equal weight versions is in howindex components are weighted.


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Uses and importance of air pollution indexand stock market index

As everyone can see,the air pollution index is use bythe government to measure the air quality index and todetect any pollutants in our countrys air.This is toensure the air is clean and safe for us to inhale.Besidesthat,an early warning can be given to us if the air

pollution is to high for us to get out of our homes. This

warning is given based upon readings andinterpretations of the air pollution 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 index isimportant because a countrys economical statesometimes depend on it.


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ConclusionAfter doing research,answering questions,drawing graphs and

some problem solving, I saw that the usage of statistics isimportant in daily life.It is not just widely used in markets butalso in interpreting the condition of the surrounding like the air orthe water.Especially in conducting an air-pollution survey.Incoclusion,statistics is a daily life nessecities.Without it,surveyscant be conducted,the stock market cant be interpret and manymore.So,we should be thankful of the people who contribute inthe idea of statistics.


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ReflectionAfter spending countless hours,day andnight to finish this AdditionalMathematics Project,here is what I gotto say:

Doing this project makes me realize howimportant Additional Mathematicsis.Also, completing this project makes

me realize how fun it is and likable isAdditional Mathematics

addmath sample 1

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