Additional Mathematics work project 2010 Statistics in Our Daily Life

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

Zuhdi Khudzairi SMAKJ 10 A+

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 nonroutine 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 administered to us.Failure to submit the written report will result in us not receiving certificate. Zuhdi Khudzairi SMAKJ 10 A+

‫الحمدل رب العالمين حمدا حامد حمد شاكرا حمد نعمه ويكافي مزيده يا ربنا لك الحمد‬ ‫ينبغي لجللك وجهك عظيم سلطانك‬ 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.

Zuhdi Khudzairi SMAKJ 10 A+

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 concerned with the scientific method and inductive logic, statistical theory has close association with the philosophy of science; with its emphasis on learning from data and making best Zuhdi Khudzairi SMAKJ 10 A+

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 as psychology, education, and public health.

Zuhdi Khudzairi SMAKJ 10 A+

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

Zuhdi Khudzairi SMAKJ 10 A+

Answer:

Zuhdi Khudzairi SMAKJ 10 A+

Zuhdi Khudzairi SMAKJ 10 A+

Zuhdi Khudzairi SMAKJ 10 A+

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.

Zuhdi Khudzairi SMAKJ 10 A+

Categor y

Item

Price(RM) Econsave

Giant

Jusco

U Mall

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)

9.75

9.99

9.50

19.45

19.43

19.35

1.Kiwi Cleen

6.9

5.49

5.50

Softlan Softener

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

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

27.70

25.39

28.60

30 eggs Total Price

Deterge nt

3 Litre

`Station Highlighter Faber Castell ery

Total Price Zuhdi Khudzairi SMAKJ 10 A+

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.

Zuhdi Khudzairi SMAKJ 10 A+

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

Zuhdi Khudzairi SMAKJ 10 A+

(a)

(b)

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. 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.

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

5 eggs (300g)

1.25

1.58

Eggs(Grade A)

Answer:

Question (i)

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

Zuhdi Khudzairi SMAKJ 10 A+

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

5 eggs (300g)

1.25

1.58

126.4

Eggs(Grade A)

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

Zuhdi Khudzairi SMAKJ 10 A+

(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: On 2009,RM 15.00

Zuhdi Khudzairi SMAKJ 10 A+

On 2010, price=ϰ15×100=117.5745% ϰ×100=117.5745×15 ϰ ϰ

=1763.6175100

=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

Zuhdi Khudzairi SMAKJ 10 A+

electrical power. It is suitable for a room size 1000ft³ which is around 27m³ 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 =999.6m³ 1 unit of air conditioner is for 27m ³ For 999.6m³=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 air conditioner? Zuhdi Khudzairi SMAKJ 10 A+

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

Zuhdi Khudzairi SMAKJ 10 A+

Answer , Expenditure

Amount in 2009

Amount in 2010

(RM)

(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

Amount in 2010

Price Index, I

(RM)

(RM)

I=P1P0×100

Weightage, W

%

Food

1200.00

Zuhdi Khudzairi SMAKJ 10 A+

1380.00

115

12

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. Solution.

Zuhdi Khudzairi SMAKJ 10 A+

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 Ī20112009

=Ī20102009×Ī20112010

=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. Obtain information from the internet or other reliable sources on the importance of two different types of index number of your Zuhdi Khudzairi SMAKJ 10 A+

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 transportation or work from home when AQI levels are high. Zuhdi Khudzairi SMAKJ 10 A+

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

0-50

Description

Good

Zuhdi Khudzairi SMAKJ 10 A+

Health Implications A level that will not impact patients suffering from diseases related to air pollution.

51100

Moderate

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

101150

Unhealthy for A level that may have harmful impacts on sensitive patients and members of sensitive groups. groups

151250

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.

Unhealthy

A level which may have a serious impact 251Very unhealthy on patients and members of sensitive 350 groups in case of acute exposure.

351500

Hazardous

Zuhdi Khudzairi SMAKJ 10 A+

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

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.

Zuhdi Khudzairi SMAKJ 10 A+

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. Zuhdi Khudzairi SMAKJ 10 A+

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 considers the price of the components, total return, which accounts for

Zuhdi Khudzairi SMAKJ 10 A+

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.

Uses and importance of air pollution index and stock market index

As everyone can see,the air pollution index is use by the government to measure the air quality index and to detect any pollutants in our country’s air.This is to ensure the air is clean and safe for us to inhale.Besides that,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 and interpretations of the air pollution index. As for the stock market index, it is mainly for the business entrepreneurs. This type of index is used to determine the Zuhdi Khudzairi SMAKJ 10 A+

outcome of a stock market and also the conclusion of a stock market. The stock market index is important because a country’s economical state sometimes depend on it.

Conclusion After doing research,answering questions,drawing graphs and some problem solving, I saw that the usage of statistics is important in daily life.It is not just widely used in markets but also in interpreting the condition of the surrounding like the air or the water.Especially in conducting an air-pollution survey.In coclusion,statistics is a daily life nessecities.Without it,surveys can’t be conducted,the stock market can’t be interpret and many more.So,we should be thankful of the people who contribute in the idea of statistics.

Zuhdi Khudzairi SMAKJ 10 A+

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

Zuhdi Khudzairi SMAKJ 10 A+

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

Zuhdi Khudzairi SMAKJ 10 A+

No

Contents

1

Introduction

2

Part 1

3

Part 2

4

Part 3

5

Part 4

6

Part 5

7

Conclusion

Zuhdi Khudzairi SMAKJ 10 A+

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