33243261 32958798 additional math ma tics project work 4 for 2010 full

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Statistics In Our Daily LifePROJECT WORK FOR ADDITIONAL MATHEMATHICS 2010Nama:Mohammad.Irwandy bin Mohammad.Jali Guru Pembimbing: Puan Rosmeela

Kolej Datu Patinggi Abang Haji Abdillah



IntroductionWe 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 onlyONE 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 valuab

le experiences and able to: y Apply and adapt a variety of problem solving strategies to solve routine and non-routine problems; y Experience classroom environments which are challenging, interesting and meaningful and hence improve their thinking skills. y Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems y Experience classroom environments where expressing ones mathematical thinking,reasoning and communication are highly encouraged and expected y Experience classroom environments that stimulates and enhances effective learning. y Acquire effective mathematicalcommunication through oral and writing,and to use the language of mathematics to express mathematical ideas correctly and precisely y Enhance acquisition of mathematical knowledge and skills through problem-solving in ways that increase interest and confidence y Prepare ourselves for the demand of our future undertaki

ngs and in workplace



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 to collaborate, to cooperate,and to share knowledge in an engaging and healthy environment y Use technologyespecially the ICT appropriately and effectively y Train ourselves to appreciatethe intrinsic values of mathematics and to become 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 first daythe task is being administered to us.Failure to submit the written report willresult in us not receiving certificate.



AppreciationAlhamdullilah,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 myAdditional 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, I would like to thank

my parents for their support and encouragement. Lastly, a special thanks to allmy friends for their help and cooperation in searching for information and completing this project work.



History of statisticBy the 18th century, the term "statistics" designated the systematic collectionof 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 ingovernment, business, and all the sciences. Electronic computers have expeditedstatistical computation, and have allowed statisticians to develop "computer-in

tensive" methods. The term "mathematical statistics" designates the mathematicaltheories 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 probabilitytheory, 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 statis

tical 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, statisticshad 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 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 todayDuring 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 useof 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 isgenerally 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.



Part 1The prices of goods sold in shops vary from one shop to another.Shoppers tend tobuy 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 thefollowing 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 Ans

wer:



Food



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. Answer:

Category

Item

Price(RM) Boulevard Everrise Discount store 4.00 2.00 4.70 5.90 16.60 3.20 4.2918.90 5.50 31.89 1.50 5.00 1.30 1.30 9.10 57.59 3.70 1.90 4.50 5.50 15.60 3.00 3.90 17.00 5.50 29.40 1.30 4.80 1.20 1.20 8.50 53.50 3.60 1.80 4.30 5.00 14.70 2.80 3.20 16.50 5.50 28.00 1.00 4.50 1.00 1.10 7.60 50.30

1.Self-Raising Flour(1000g) Food 2.Sugar(1000g) 3.Butter(250g) 4.Eggs(Grade A) 1dozen Total Price 1.Soap(3 bars) Detergent 2.Liquid dishwasher(1000ml) 3.Clothes detergent(3kg) 4.Toilet cleaner(500ml) Total Price 1.Sharpener Stationery 2.Pencil (2B-1 dozen) 3.Pen 4.Eraser Total Price Grand Total



Question(c) Create at least two suitable graphical representations (the use of ICT is encouraged) to compare and contrast the price of the items chosen. Answer: 1)7

6

5

4

Self-raising flourSugar

3

Butter

Eggs(Grade A) 2

1

0Boulevard Everrise Discount store



2)20 18

16

14

12

Soa (3 ar)10

Liquid dishwasher(1000ml)Toilet cleaner(500ml)

8

Clothes detergent(3 kg)

6

4

2

0Boulevard Everrise Discount store

¡



3)6

5

4

Sharpener

Eraser

2

1

0 Boulevard Everrise Discount store

¢ ¢

3

e ncil 2B(1 Dozen) en



Question (d) Based on the graphical representation that you have constructed inPart 1(c), interpret,discuss and draw conclusions. Comments on your findings.

Answer: Based on the graphical representations that I have constructed in Part 1(c), it is shown that there are large and small differences among the prices ofitems in each category between the shops.In the food category, the smallest price difference are of those of sugar, while the highest is the price of eggs. Besi

des food, detergent also shows a large price difference between its items. Amongthem is the price of liquid dishwasher and clothes detergent. On the other hand,stationery items doesn¶t have any obvious price difference. The graph also showthat most of the items that are high priced comes from the Boulevard Supermarket, while the lowest price items come from the Discount Store.The graph 1(d) willshow the conclusion of the difference among the shops based upon the shops grand total.



60

58

56

54 Boulevard Everrise 52 Discount store

50

48

46Grand total

Graph 1(d)



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: Liquid dishwasher: Mean= =17.47 Standard deviation = ¥( ²)/N ± ( =¥ =0.97 The large price difference of clothes detergent among the shops maybe because of the standard of theshop.A high standard shop or supermarket, the items sold intend to be much moreexpensive than a regular shop or supermarket.Also, the price difference of the i

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

)²

- (17.47)²



Part 2Every 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 projectfor this year¶s carnival. Question (a) Suggest a shop from Part 1 which you would go to purchase the ingredients for the butter cakes.State and discuss your re

asons for purchasing from the shop you suggested.

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

Question (b) Answer: Quantity Per cake Self-raising flour 250g Sugar 200g Butter250g Eggs(Grade A) 5 eggs (300g) Ingredient Price in the year 2009(RM) 0.90 0.35 3.30 1.25 Price in the year 2010(RM) 0.90 0.36 4.30 2.10 Complete Table 2 withthe prices of the items found in the shop/supermarket that you have chosen.



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

Answer: Ingredient Quantity Per cake Price in the year 2009(RM) 0.90 0.35 3.30 1.25 Price in the year 2010(RM) 0.90 0.36 4.30 2.10 Price index for the year 2010based on the year 2009 () 100 102.86 130.30 168

Self-raising flour Sugar Butter Eggs(Grade A)

250g 200g 250g 5 eggs (300g)

1.Self-raising flour=

2.Sugar=

3.Butter=

4.Eggs(Grade A)=



Question (ii) Calculate the composite index for making a butter cake in the year2010 based on the year 2009. Discuss how you obtained your answers. Answer: Tocalculate the composite index,weightage is needed (W),

Ingredients Weightage (W) Self-raising flour Sugar Butter Eggs(Grade A)

Composite index

=128.54



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 On 2010, price=

=

=19.30Thus,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.



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), whichis approximately 700W to 1000W of electrical power. It is suitable for a room size 1000ft which is around 27m 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 requi

red for your library. 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. 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? 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 =RM11.64 Number of cakes to buy

1 unit of air conditioner = = 60.13 = 60 cakes



Part 3As a committee member for the carnival, you are required to prepare an estiatedbudget 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. Answer , Expenditure Food Games Transportation Decorations Prizes Tents Miscellaneous Amountin 2009 (RM) 1200.00 500.00 300.00 200.00 600.00 800.00 400.00 Table 3 Amount in 2010 (RM) 1380.00 500.00 345.00 200.00 600.00 920.00 520.00



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 Amount Price Weightage, in 2009 in 2010 Index, W (RM) (RM) I I= 1200.00 500.00 300.00 200.00 600.00 800.00 400.00 1380.00 500.00 345.00 200.00 600.00 920.00 520.00 115 100 115 100 100 115 130 12 5 3 2 6 8 4

Food Games Transportation Decorations Prizes Tents Miscellaneous

Composite Index = = = =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 theyear 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. 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

E

=111.625 111.625 124.60



Further ExplorationIndex numbers are being used in many different daily situations, for example airpollution 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 choice. Elaborate the use and the importance of these index numbers in daily life.



Air Pollution IndexAir 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 tosupport life on planet Earth. Stratospheric ozone depletion due to air pollutionhas 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 rangeis assigned a descriptor and a color code. Standardized public health advisoriesare 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. Limitations of the AQI Most air contaminants do not have an associated AQI.

Many countries monitor ground-level ozone, particulates, sulphur dioxide, carbonmonoxide 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 anticycloneor temperature inversion, or other lack of winds lets air pollution remain in alocal area.



Indices by locationSouth 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 qualitylevel and protect the health of people from air pollution. - The CAI has valuesof 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 pollutan

ts, 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.

51100

Moderate

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

101150

Unhealthy for sensitive groups

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

151250

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 unpleasantfeelings.

251350

Very unhealthy

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

351500

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.



MalaysiaThe air quality in Malaysia is reported as the API or Air Pollution Index. Fourof the index's pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulfur dioxide) are reported in PM10 particulate matter is reported in g/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 c

losed. There may also be a prohibition on private sector commercial and industrial activities in the reporting area excluding the food sector.



St

M

t Index

A compari on of t ree major U.S. stock indices: t eNASDAQ Composite, Dow Jones I

ndustrial Average, andS&P 500. All t ree 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 i ex is a method of measuring a sectionof the stock market. Many indices are cited by news or financial services firmsand are used as benchmarks, to measure the performance of portfolios such as mutual funds. 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 Worldand S&P Global 100. A national index represents the performance of the stock market of a given nation²and by proxy, reflects investor sentiment on the state ofits economy. The most regularly quoted market indices are national indices composed of the stocks of large companies listed on a nation's largest stock exchange

s, 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 one index management, or even more specialized criteria published by Linux Weekly News tracks stocks of companies that sell products and services based on the Linux operating environment.

Index versionsSome indices, such as the S&P 500, have multiple versions.[1] These versions candiffer based on how the index components are weighted and on how dividends areaccounted for. For example, there are three versions of the S&P 500 index: pricereturn, which only considers the price of the components, total return, which accounts for 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 areweighted.



Uses and importance of air pollution index and stock market indexAs everyone can see,the air pollution index is use by the government to measurethe air quality index and to detect any pollutants in our country¶s air.This isto 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 ent

repreneurs. This type of index is used to determine the outcome of a stock market and also the conclusion of a stock market. The stock market index is importantbecause a country¶s economical state sometimes depend on it.



ConclusionAfter 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 surroundinglike 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.



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

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

33243261 32958798 additional math ma tics project work 4 for 2010 full

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