hanee's project work (add math task 4)

8/9/2019 Hanee's Project Work (ADD MATH TASK 4)

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Statistic In Our Daily Life

PROJECT WORK FOR ADDITIONAL MATHEMATICS 2010

Name:

Class:

Ic Number:

School:

Advisor:


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Introduction We students taking Additional Mathematics are required to carry out a project

work while we are in Form 5.This year the Curriculum Development Division,

Ministry of Education has prepared four tasks for us.We are to choose andcomplete only ONE task based on our area of interest.This project can be done ingroups or individually,but each of us are expected to submit an individually writtenreport.Upon completion of the Additional Mathematics Project Work,we are togain valuable experiences and able to:

y Apply and adapt a variety of problem solving strategies to solve routineand non-routine problems;

y Experience classroom environments which are challenging, interesting andmeaningful and hence improve their thinking skills.

y Experience classroom environments where knowledge and skills areapplied in meaningful ways in solving real -life problems

y Experience classroom environments where expressing ones mathematicalthinking,reasoning and communication are highly encouraged andexpected

y Experience classroom environments that stimulates and enhances effectivelearning.

y Acquire effective mathematical communication through oral andwriting,and to use the language of mathematics to express mathematicalideas correctly and precisely

y Enhance acquisition of mathematical knowledge and skills throughproblem-solving in ways that increase interest and confidence

y Prepare ourselves for the demand of our future undertakings and inworkplace

y Realise that mathematics is an important and powerful tool in solving real -life problems and hence develop positive attitude towards mathematics.

y Train ourselves not only to be independent learners but also tocollaborate, to cooperate, and to share knowledge in an engaging andhealthy environment

y Use technology especially the ICT approp riately and effectivelyy

Train ourselves to appreciate the intrinsic values of mathematics and tobecome more creative and innovativey Realize the importance and the beauty of mathematics

We are expected to submit the project work within three weeks from the firstday the task is being administered to us.Failure to submit the written reportwill result in us not receiving certificate.


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Appreciation

Alhamdullilah, thank you to Allah for giving the will to do myadditional mathematics project. Secondly, I would like to thank theprinciple of Sekolah Menengah Kebangsaan Telok Panglima Garang,Tuan Haji Nordin bin Saad for giving the permission to do my AdditionalMathematics Project Work. I also like to thank my AdditionalMathematics teacher, Miss Rojita for the guide and giving useful andimportant information for me to complete this project work. Besidesthat, I would like to thank my parents for their support andencouragement. Lastly, a special thanks to all my friends for their helpand cooperation in searching for information and completing thisproject work.


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History of statisticBy the 18th century, the term "statistics" designated the systematiccollection of demographic and economic data by states. In theearly 19th century, the meaning of "statistics" broadened, thenincluding the discipline concerned with the collection, summary, and

analysis of data. Today statistics is widely employed in government,business, and all the sciences. Electronic computers haveexpedited statistical computation, and have allowed statisticians todevelop "computer-intensive" methods.

The term "mathematical statistics" designates the mathematicaltheories of probability and statistical inference, which are usedin statistical practice. The relation between statistics and probabilitytheory developed rather late, however. In the 19th century, statisticsincreasingly used probability theory, whose initial results were found inthe17th and 18th centuries, particularly in the analysis of games ofchance (gambling). By 1800, astronomy used probability models andstatistical theories, particularly the method of least squares, whichwas invented by Legendre and Gauss. Early probability theory andstatistics was systematized and extended by Laplace; followingLaplace, probability and statistics have been in continualdevelopment. In the 19th century, social scientists used statisticalreasoning and probability models to advance the new sciencesof experimental psychology and sociology; physical scientists usedstatistical reasoning and probability models to advance the newsciences of thermodynamics and statistical mechanics. Thedevelopment of statistical reasoning was closely associated with thedevelopment of inductive logic and the scientific method.

Statistics is not a field of mathematics but anautonomous mathematical science, like computer science oroperations research. Unlike mathematics, statistics had its originsin public administration and maintains a special concern

with demography and economics. Being concerned with the scientificmethod and inductive logic, statistical theory has close associationwith the philosophy of science; with its emphasis on learning from dataand making best predictions, statistics has great overlap withthe decision science and microeconomics. With its concerns with data,statistics has overlap with information science and computer science.


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Statistic todayDuring the 20th century, the creation of precise instrumentsfor agricultural research, public health concerns(epidemiology, biostatistics, etc.), industrial quality control, andeconomic and social purposes (unemployment rate, econometry, etc.)necessitated substantial advances in statistical practices.

Today the use of statistics has broadened far beyond its origins.Individuals and organizations use statistics to understand data andmake informed decisions throughout the natural and social sciences,medicine, business, and other areas.

Statistics is generally regarded not as a subfield of mathematics but

rather as a distinct, albeit allied, field. Many universities maintainseparate mathematics and statistics departments. Statistics is alsotaught in departments as diverse as psychology, education, and publichealth


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Part 1The prices of goods sold in shops very from one shop to another.Shoppers tend to buy goods which are not only reasonably priced butalso give value for their money.

You are required to carry out a survey on four different items based onthe 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:

Food

Detergent

Stationary


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Q uestion

(c) Create at least two suitable graphical representations (the use ofICT is encouraged) to compare and contrast the price of the itemschosen.

Answer:

1) Food

2) Detergent

0

1

2

3

4

5

6

7

Jaya Jusco Tesco Econsave

Self-raising flour

Sugar

Butter

Eggs(Grade A)

0

2

4

6

8

10

12

14

16

18

20

Jaya Jusco Tesco Econsave

Soap(3 bar)

Liquiddishwasher(1000ml)

Toilet cleaner(500ml)

Clothes detergent(3kg)


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3) Stationary

Q uestion

(d) Based on the graphical representation that you have constructedin Part 1(c), interpret,discuss and draw conclusions. Comments on yourfindings.

Answer:

Based on the graphical representations that I have constructed in Part1(c), it is shown that there are large and small differences among theprices of items in each category between the shops.In the foodcategory, the smallest price difference are of those of sugar, while thehighest is the price of eggs. Besides food, detergent also shows a largeprice difference between its items. Among them is the price of liquid

dishwasher and clothes detergent. On the other hand,stationery itemsdoesnt have any obvious price difference. The graph also show thatmost of the items that are high priced comes from the Jaya JuscoSupermarket, while the lowest price items come from the EconsaveStore.The graph 1(d) will show the conclusion of the difference amongthe shops based upon the shops grand total.

0

1

2

3

4

5

6

Jaya J sc Tesc Ec save

S

ar e er

Pe cil 2B(1 D ze )

Pe

Eraser


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Graph 1(d)

Q uestion

(e) Identify an item that has a large price differenceamong the shops. Calculate the mean and standard deviation of thatparticular item. Hence, suggest and discuss possible reasons for theprice difference.

Answer:

Liq u id di shw a sh er:

Mean=

=17.47

Standard deviation

= ( )/N (

)

= - (17.47)

=0.97

The large price difference of clothes detergent among the shopsmaybe because of the standard of the shop. A high standard shop orsupermarket, the items sold intend to be much more expensive than aregular shop or supermarket. Also, the price difference of the itemsmay also due to the quality of the item present. A better qualitymeans a higher price.

46

48

50

52

54

56

58

60

ra t tal

Jaya Jusc

Tecs

Ec save


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Part 2Every year SMKTPG organises a carnival to raise funds for the school.This year the school plans to install air conditioners in the school

library. Last year, during the carnival, your class made and sold buttercakes. Because of the popularity of the butter cakes,your class hasdecided to carry out the same project for this years carnival.

Q uestion:

(a) Suggest a shop from Part 1 which you would go to purchase theingredients for the butter cakes.State and discuss your reasons forpurchasing from the shop you suggested.

Answer:

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

Q uestion:

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

Answer:

Ingredient Q uantityPer cake

Price in the year2009( RM)

Price in theyear 2010( RM)

Self-raisingflour 250g 0.90 0.90

Sugar 200g 0.35 0.36Butter 250g 3.30 4.30Eggs(Grade A) 5 eggs (300g) 1.25 2.10


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Q u e s tion

(ii) Cal cu late t h e c ompo s i te index for making a b u tter c ake in t h e year 2010ba s ed on t h e year 2009. Di scuss h ow yo u obtained yo u r an sw er s .

Answ er:

To c al cu late t h e c ompo s ite index, w eig h tage i s needed (W),

Ingredient s Weig h tage (W)Self-rai s ing

flo u r

Su gar

Bu tter

Eggs (GradeA)

Compo s ite index

=128.54

Q u e s tion

(iii) In t h e year 2009,t h e b u tter c ake w a s s old at RM15.00 ea ch .S u gge s t asu itable s elling pri c e for t h e b u tter c ake in t h e year 2010.Give rea s on s for yo u r an sw er.

Answ er:

On 2009,RM 15.00

On 2010, pri c e=

=

=19.30Thus ,t h e su itable pri c e for t h e b u tter c ake for t h e year 2010 i s RM19.30.T h e

in c rea s e in pri c e i s al s o su itable be c a us e of t h e ri s e in t h e pri c e of t h e

ingredient s .


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Q uestion

(c)(i) Find out from reliable sources how to determine suitablecapacity of air conditioner to be installed based on the volume/size ofa room.

Answer:

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

Q uestion

(ii) Work in groups to estimate the volume of your school library.Explain how you arrive at your answer. Hence, determine the numberof air conditioners with the appropriate capacity required for yourlibrary.

Answer:

By using a measuring tape,the dimension for the library is:

Height=3.6m

Width=9.17m

Length=20.12m

Volume of the room=3.6 9.17 20.12

=664.20m

1 unit of air conditioner is for 27m

For 664.20m =

=24.6

That means our school library needs 25 unit of air conditioner.


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Q uestion

(iii) If your class intends to sponsor one air conditioner for the schoollibrary, how many butter cakes must your class sell in order to buy theair conditioner?

Answer:

1 unit of 1HP air conditioner= RM700

Cost 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 are required to preparean estiated budget to organize this years carnival. The committee hasto take into the consideration the increase in expenditure from theprevious year due to inflation. The price of food, transportation andtents has increased by 15%. The cost of games, prizes and decorationsremains the same, whereas the cost of miscellaneous items hasincrease by 30%.

Q uestion

a) Complete Table 3 based on the information given above.

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

Q uestion

b) Calculate the composite index for the estimated budget of thecarnival in the year 2010 based on the year 2009. Comment onyour answer.


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Further ExplorationIndex numbers are being used in many different daily situations, forexample air pollution index, stock market index, gold index andproperty index.

Obtain information from the internet or other reliable sources on theimportance of two different types of index number of your choice.Elaborate the use and the importance of these index numbers in dailylife.


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Air Pollution IndexAir poll u tion is the introduction of chemicals, particulate matter,or biological materials that cause harm or discomfort to humans orother living organisms, or damages the natural environment intothe atmosphere.

The atmosphere is a complex dynamic natural gaseous system that isessential to support life on planet Earth. Stratospheric ozonedepletion due to air pollution has long been recognized as a threat tohuman health as well as to the Earth's ecosystems.

The Air Q u ality Index (AQ I) (also known as the Air Poll u tionIndex (API) or Poll u tant Standard Index (PSI) is a number used bygovernment agencies to characterize the quality of the air at a given

location. As the A Q I increases, an increasingly large percentage of thepopulation is likely to experience increasingly severe adverse healtheffects. To compute the A Q I requires an air pollutant concentrationfrom a monitor or model. The function used to convert from airpollutant concentration to A Q I varies by pollutant, and is different indifferent countries. Air quality index values are divided into ranges,and each range is assigned a descriptor and a color code. Standardizedpublic health advisories are associated with each A Q I range. An agencymight also encourage members of the public to take public

transportation or work from home when A Q I levels are high.

Limitations of the A Q I

Most air contaminants do not have an associated A Q I. Many countriesmonitor ground-level ozone, particulates, sulphur dioxide, carbonmonoxide and nitrogen dioxide and calculate air quality indices forthese pollutants.

Causes of Poor Air Q ualityThe A Q I can worsen (go up) due to lack of dilution of air emissions byfresh air. Stagnant air, often caused by an anticyclone or temperatureinversion, or other lack of winds lets air pollution remain in a localarea.


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Indices by location

Sou t h 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 easilyunderstand air quality level and protect the health of people from airpollution. - The CAI has values of 0 through 500, which are divided intosix categories. The higher the CAI value, the greater the level of airpollution. - Of values of the five air pollutants, the highest is the CAIvalue.

CAI Desc ription Healt h Impli c ation s

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 onpatients in case of chronic exposure.

101-150

Unhealthy forsensitive groups

A level that may have harmful impacts onpatients and members of sensitive groups.

151-250 Unhealthy

A level that may have harmful impacts onpatients and members of sensitive groups(children, aged or weak people), and also causethe general public unpleasant feelings.

251-350 Very unhealthy

A level which may have a serious impact onpatients and members of sensitive groups incase of acute exposure.

351-500 Hazardous

A level which may need to take emergencymeasures for patients and members of sensitivegroups and have harmful impacts on the generalpublic.


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consists of 36 American firms in the biotechnology industry. Otherindices may track companies of a certain size, a certain type ofmanagement, or even more specialized criteria i one index publishedby Linux Weekly News tracks stocks of companies that sell productsand 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, which onlyconsiders the price of the components, total return, which accountsfor dividend reinvestment, and net total return, which accounts fordividend reinvestment after the deduction of a withholding tax. As

another example, the Wilshire 4500 and Wilshire 5000 indices have fiveversions each: full capitalization total return, full capitalization price,float-adjusted total return, float-adjusted price, and equal weight.The difference between the full capitalization, float-adjusted, andequal weight versions is in how index components are weighted.


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Uses and importance of air pollutionindex and stock market index

As everyone can see,the air pollution index is use by thegovernment to measure the air quality index and to detect anypollutants in our countrys air.This is to ensure the air is clean and safefor us to inhale.Besides that,an early warning can be given to us if theair pollution is to high for us to get out of our homes. This warning isgiven based upon readings and interpretations of the air pollution

index.

As for the stock market index, it is mainly for the businessentrepreneurs. This type of index is used to determine the outcome ofa stock market and also the conclusion of a stock market. The stockmarket index is important because a countrys economical statesometimes depend on it.


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Conclusion

After doing research,answering questions,drawing graphs andsome problem solving, I saw that the usage of statistics isimportant in daily life. It is not just widely used in marketsbut also in interpreting the condition of the surrounding likethe air or the water. Especially in conducting an air-pollutionsurvey. In conclusion, statistics is a daily life nessecities.Without it,surveys cant be conducted,the stock market cantbe interpret and many more. So,we should be thankful of thepeople who contribute in the idea of statistics.


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Reflection

After spending countless hours,day and night to finish thisAdditional Mathematics Project, here is what I got to say:

Doing this project makes me realize how important AdditionalMathematics is. Also, completing this project makes me realizehow fun it is and likable is Additional Mathematics

hanee's project work (add math task 4)

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