Additional Mathematics work project 2010 Statistics in Our Daily Life

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Statistics In Our Daily

Life

Project Work For Additional

Mathematics 2010

Nama: Ahmad Zuhdi Bin Md Khudzari

Kelas:5 Ibnu Sina

Guru Pembimbing:Cikgu Ghozi Bin Md Nor.

Sekolah Menengah Agama Kerajaan Johor

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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 and complete only ONE task based on our area of interest.This project can be done in groups or individually,but each of us are expected to submit an individually written report.Upon completion of the Additional Mathematics Project Work,we are to gain valuable experiences and able to:

• Apply and adapt a variety of problem solving strategies to solve routine and

non-routine problems;

• Experience classroom environments which are challenging, interesting and meaningful

and hence improve their thinking skills.

• Experience classroom environments where knowledge and skills are applied in

meaningful ways in solving real-life problems

• Experience classroom environments where expressing ones mathematical

thinking,reasoning and communication are highly encouraged and expected

• Experience classroom environments that stimulates and enhances effective learning.

• Acquire effective mathematical communication through oral and writing,and to use the

language of mathematics to express mathematical ideas correctly and precisely

• Enhance acquisition of mathematical knowledge and skills through problem-solving in

ways that increase interest and confidence

• Prepare ourselves for the demand of our future undertakings and in workplace

• Realise that mathematics is an important and powerful tool in solving real-life

problems and hence develop positive attitude towards mathematics.

• Train ourselves not only to be independent learners but also to collaborate, to

cooperate, and to share knowledge in an engaging and healthy environment

• Use technology especially the ICT appropriately and effectively

• Train ourselves to appreciate the intrinsic values of mathematics and to become more

creative and innovative

• Realize the importance and the beauty of mathematics.

We are expected to submit the project work within three weeks from the first day the task is being

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دمحلا كل انبر اي هديزم يفاكيو همعن دمح اركاش دمح دماح ادمح نيملاعلا بر لدمحلا كناطلس ميظع كهجو كللجل يغبني

Feeling Blessed By Allah S.w.T and Nabi Muhammad Al-Mustofa S.A.W because give me the willingness to perform this project completely.Secondly,I want to thanked to my principle Ustaz Maskon Bin Kadan because give me permission to complete this project during school holidays.Then,I want to thanked to my Additional Mathematics

Teacher,Cikgu Ghozi Bin Md Nor because give me best guidance and support to do this Additional Mathematics Project.By the way,I want to thanked to my lovely parent Haji Khudzairi Abd Jabar and Hajah Azizah Abd Manap because give me support and

encouragement to complete this Additional Mathematics project.Last but not least,I want to thanked to all my friend and everybody that helped me in order to complete this Additional Mathematics Project because without all of you I cannot done this work individually successly.

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History of statistic

By the 18th century, the term "statistics" designated the systematic

collection of demographic and economic data by states. In the early 19th century, the meaning of "statistics" broadened, then including 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 have expedited statistical computation, and have allowed statisticians to develop "computer-intensive" methods.

The term "mathematical statistics" designates the mathematical theories

of probability and statistical inference, which are used in statistical practice. The relation 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 used probability models and statistical theories, particularly the method of least squares, which was invented by Legendre and Gauss. Early probability theory and statistics was systematized and extended by Laplace; following Laplace, probability and statistics have been in continual development. In the 19th century, social scientists used statistical reasoning and probability models to advance the new sciences of experimental psychology and sociology; physical scientists used statistical reasoning and probability models to advance the new sciences of thermodynamics and statistical mechanics. The development of statistical reasoning was closely associated with the development of inductive logic 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 had its origins in public administration and maintains a special concern with demography and economics. Being

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predictions, statistics has great overlap with the decision science and microeconomics. With its concerns with data, statistics has overlap with information science and computer science.

Statistics today

During the 20th century, the creation of precise instruments for agricultural research, public health concerns (epidemiology, biostatistics, etc.), industrial quality control, and economic 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 and make 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 maintain separate mathematics and

statistics departments. Statistics is also taught in departments as diverse

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Part 1

The prices of goods sold in shops vary from one shop to

another.Shoppers tend to buy goods which are not only reasonably priced but also give value for their money.

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

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

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Question

(b) Record the items and their prices systematically as in Table

1.Since items maybe differently packed,be sure to use consistent

measurements for each item selected so that comparison can be

done easily and accurately.

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Categor

y

Item Price(RM) Econsave Giant U Mall Jusco

Food

1.Self-Raising Flour(1000g) 4.00 3.70 3.60 2.Sugar(1000g) 1.75 1.75 1.75 3.Butter(250g) 3.95 3.99 4.50 4.Eggs(Grade A) 30 eggs 9.75 9.99 9.50 Total Price 19.45 19.43 19.35

Deterge

nt

1.Kiwi Cleen 6.9 5.49 5.50 Softlan Softener 3 Litre 6.29 9.99 6.99 3.Daia 1 Kg 4.69 5.49 5.50 4.Breeze Liquid Colour 1.8 Kg 10.30 10.99 10.70 Total Price 28.18 31.96 28.69 `Station ery Highlighter Faber Castell 3.50 3.49 3.70 Staedler Water Colour 13.50 10.00 13.50

Stabilo Liquid Paper 3.50 3.90 3.90

Faber Castell Pencil Tri Grip Pencill

7.20 8.00 7.50

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Question:Create at least two suitable graphical representations

(the use of ICT is encouraged)to compare and contrast the prices

of the items chosen.

Question

(d) Based on the graphical representation that you have

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

conclusions. Comments on your findings.

Based on the graph we could see the small and large diferrence among the

items.We could see from food price the lowest price is sugar because sugar is now known as controlled goods so there are no such difference among them and the highest price is eggs grade A.All of us know the difference among eggs and

another item is because the controlled standard to this eggs which caused the price so high than another food items.MoreOver,when we look to detergent the lower price is Daia that have quantity about 1 kg and the higher price is Breeze Liquid Colour this is because the difference detergebt bring the difference price.On the other hand,the lowest price among stationery items is highlighter faber castell and the highest price among them is staedler water colour.I think it is because the standard and quality that given by staedler to users.All of this can be conclused with the grand total.

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Question

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

Answer:Softlan 3L 6.29+9.99+6.99÷3 =7.756 Standard deviation = √(∑х²)/N – ( х ̃ )² = √ 6.29²+9.99²+6.99²3 - (7.756)²

=

1.965536

The large difference among the price is because the standard of the shop.So,the more standard of the supermarket,the higher the price given to the users.The Higher the price the higher quality u can get from that product.

Part 2

Every year SMK Indah 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 butter cakes. Because of the popularity of the butter cakes,your class has decided to carry out the same project for this year’s

carnival. Question

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

(b) I choose Jusco because it offers me the lowest total prica among the food items

Question

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

Answer:

Question

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

Ingredient Quantity

Per cake

Price in the year 2009(RM) Price in the year 2010(RM) Self-raising flour 250g 0.90 0.90 Sugar 200g 0.35 0.35 Butter 250g 3.30 4.50 Eggs(Grade A) 5 eggs (300g) 1.25 1.58

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1.Self-raising flour

Ι=0.90.9×100=100

2.Sugar

Ι=0.350.35×100=100

3.Butter

Ι=4.53.3×100=136.33

4.Eggs(Grade A)

Ι=1.581.25×100=126.4

Question

Ingredient Quantity Per cake Price in the year 2009(RM) Price in the year 2010(RM)

Price index for the year 2010 based on the year 2009 (Ι) Self-raising flour 250g 0.90 0.90 100 Sugar 200g 0.35 0.35 102.86 Butter 250g 3.30 4.50 136.33 Eggs(Grade A) 5 eggs (300g) 1.25 1.58 126.4

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(ii) Calculate the composite index for making a butter

cake in the year 2010 based on the year 2009. Discuss

how you obtained your answers.

Answer:

To calculate the composite index,weightage is needed

(W),

WeightTotal weight

Ingredients

Weightage (W)

Self-raising flour

2501000=14

Sugar

2001000=15

Butter

2501000=14

Eggs(Grade A)

3001000=310

Composite index

=14100+15100+14136.33+310126.41

=117.5745

Question

(iii)

In the year 2009,the butter cake was sold at RM15.00

each.Suggest a suitable selling price for the butter cake in the year 2010.Give reasons for your answer.

Answer:

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On 2010, price=

ϰ15×100=117.5745%

ϰ×100=117.5745×15

ϰ

=

1763.6175100

ϰ

=17.63

Thus,the suitable price for the butter cake for the year 2010 is

RM17.63.The increase in price is also suitable because of the

rise in the price of the ingredients.

Question

(c)(i) Find out from reliable sources how to determine suitable

capacity of air conditioner to be installed based on the

volume/size of a room.

Answer:

For common usage,air conditioner is rated according to horse

power (1HP), which is approximately 700W to 1000W of

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electrical power. It is suitable for a room size 1000ft

³

which is

around 27m

³

of volume.

Question

(ii) Work in groups to estimate the volume of your school

library. Explain how you arrive at your answer. Hence,

determine the number of air conditioners with the appropriate

capacity required for your library.

Answer:

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

Height:4.2m

Width=11.2m

Length=21.25m

Volume of the room=4.2

×11.2×21.25

=999.6m

³

1 unit of air conditioner is for 27m

³

For 999.6m

³

=

999.627

=37.02

That means our school library needs 37 unit of air conditioner.

Question

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

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Answer:

1 unit of 1HP air conditioner=RM700

Cost for a cake =0.9+0.35+4.50+1.58=7.33 Selling price =RM17.63

Profit =17.63-7.33 =RM10.30

Number of cakes to buy 1 unit of air conditioner = 70010.30 = 67.96 = 68 cakes

Part 3

As a committee member for the carnival, you are required to prepare an estiated budget to organize this year’s carnival. The committee has to take into the consideration the increase in expenditure from the previous year due to inflation. The price of food, transportation and tents has

increased by 15%. The cost of games, prizes and decorations remains the same, whereas the cost of miscellaneous items has increase by 30%.

Question,

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Answer , Expenditure Amount in 2009 (RM) Amount in 2010 (RM) Food 1200.00 1380.00 Games 500.00 500.00 Transportation 300.00 345.00 Decorations 200.00 200.00 Prizes 600.00 600.00 Tents 800.00 920.00 Miscellaneous 400.00 520.00 Table 3 Question

b) Calculate the composite index for the estimated budget of the carnival in the year 2010 based on the year 2009. Comment on your answer. Solution. Expenditure Amount in 2009 (RM) Amount in 2010 (RM) Price Index, I I=P1P0×100 % Weightage, W

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Games 500.00 500.00 100 5 Transportation 300.00 345.00 115 3 Decorations 200.00 200.00 100 2 Prizes 600.00 600.00 100 6 Tents 800.00 920.00 115 8 Miscellaneous 400.00 520.00 130 4 Composite Index Ī = ∑IiWi∑W =11512+1005+1153+1002+1006+1158+130(4)(12+5+3+2+6+8+4) =446540 =111.625

The total price for the year 2010 increase by 11.625%. This is

because some price in the year 2009 increased in the year 2010.

Question.

c) The change in the composite index for the estimate budget

for the carnival from the year 2009 to the year 2010 is the

same as the change from the year 2010 to the year 2011.

Determine the composite index of the budget for the year

2011 based on the year 2009.

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Composite index for the year 2009 to the year 2010

=111.625

Composite index for the year 2010 to the year 2011

=111.625

Ī20112009×100

=

Ī20102009×Ī20112010 Ī20112009

=111.625

×

111.625

×1100 Ī20112009=

124.60 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.

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choice. Elaborate the use and the importance of these index

numbers in daily life

.

Air Pollution Index

Air pollution is the introduction of chemicals, particulate

matter, or biological materials that cause harm or discomfort to

humans or other living organisms, or damages the natural

environment into the atmosphere.

The atmosphere is a complex dynamic natural gaseous system

that is essential to 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 the Earth's ecosystems.

The Air Quality Index (AQI) (also known as the Air Pollution

Index (API) or Pollutant Standard Index (PSI) is a number

used by government agencies to characterize the quality of the

air at a given location. As the AQI increases, an increasingly

large percentage of the population is likely to experience

increasingly severe adverse health effects. To compute the AQI

requires an air pollutant concentration from a monitor or model.

The function used to convert from air pollutant concentration to

AQI varies by pollutant, and is different in different countries.

Air quality index values are divided into ranges, and each range

is assigned a descriptor and a color code. Standardized public

health advisories are associated with each AQI range. An agency

might also encourage members of the public to take public

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Limitations of the AQI

Most air contaminants do not have an associated AQI. 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 by

an anticyclone or temperature inversion, or other lack

of winds lets air pollution remain in a local area.

Indices by location

South Korea

The Ministry of Environment of South Korea uses the

Comprehensice Air-quality Index (CAI) to describe the ambient

air quality based on health risk of air pollution. The index aims

to help the public easily understand air quality level and protect

the health of people from air pollution. - The CAI has values of

0 through 500, which are divided into six categories. The higher

the CAI value, the greater the level of air pollution. - Of values

of the five air pollutants, the highest is the CAI value.

CAI Description

Health Implications

0-50

Good

A level that will not impact patients

suffering from diseases related to air

pollution.

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51-100

Moderate

A level which may have a meager impact

on patients in case of chronic exposure.

101-150

Unhealthy for

sensitive

groups

A level that may have harmful impacts on

patients and members of sensitive groups.

151-250

Unhealthy

A level that may have harmful impacts on

patients and members of sensitive groups

(children, aged or weak people), and also

cause the general public unpleasant

feelings.

251-350

Very unhealthy

A level which may have a serious impact

on patients and members of sensitive

groups in case of acute exposure.

351-500

Hazardous

A level which may need to take

emergency measures for patients and

members of sensitive 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 Pollution Index. Four of the index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulfur dioxide) are reported in PM10 particulate

matter is reported in μg/m³.

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

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Stock Market Index

A comparison of three major U.S. stock indices: theNASDAQ

Composite, Dow Jones Industrial Average, andS&P 500. All three have the same height at March 2007. Notice the large dot-com spike on the NASDAQ, a result of the large number of tech. companies on that 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.

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Types of indices

Stock market indices may be classed in many ways. A 'world' or 'global' stock market index includes (typically large) companies without regard for where they are 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 nation—and by proxy, reflects investor sentiment on the state of its economy. The most regularly quoted market indices are national indices composed of the stocks of large companies listed on a nation's largest stock exchanges, such as the American S&P 500, the

Japanese Nikkei 225, and the British FTSE 100.

The concept may be extended well beyond an exchange. The Dow Jones Total Stock Market Index, as its name implies, represents the stocks of nearly every publicly traded company in the United States, including all U.S. stocks traded on the New York Stock Exchange (but not ADRs) and most traded on the NASDAQ and American Stock

Exchange. Russell Investment Group added to the family of indices by launching the Russell Global Index.

More specialised indices exist tracking the performance of specific sectors of the market. The Morgan Stanley Biotech Index, for example, consists of 36 American firms in the biotechnology industry. Other indices may track companies of a certain size, a certain type of

management, or even more specialized criteria — one index published 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]_These

versions can differ based on how the index components

are weighted and on how dividends are accounted for. For example, there are three versions of the S&P 500 index: price return, which only

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dividend reinvestment, and net total return, which accounts for dividend reinvestment after the deduction of a withholding tax. As another

example, the Wilshire 4500 and Wilshire 5000 indices have five versions 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, and equal weight versions is in how index components are weighted.