Add Maths Project Work 2010

8/8/2019 Add Maths Project Work 2010

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Contents

TOPIC PAGEIntroduction 1-2

Appreciation 3

A Brief History of Statistics 4

Statistics Today 5Part 1 6-11

Part 2 12-16

Part 3 17-19

Further Exploration

-Air Pollution Index

-Limitation of the AQI-Causes of Poor Air Quality

-Indices by Location

-Stock Market Index

-Types of Indices

- Index Versions

-Uses and Importance of AirPollution Index and Stock Market

Index

20-26

Conclusion 27

Reflection 28


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PROJECT WORK FOR ADDITIONAL

MATHEMATHICS 2010

CURRICULUM DEVELOPMENT DIVISION

MINISTRY OF EDUCATION MALAYSIA

PROJECT WORK 4

STATISTICS

NAME: NGEH CHEE JEN

CLASS: 5 PUTIH

IC NUMBER: 931026-08-6099

SUBJECT TEACHER: MR AZMI BIN NAZAR

SEKOLAH MENENGAH KEBANGSAAN METHODIST

AYER TAWAR


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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, and I gladly choose to do thisindividually. 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 s trategies 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 a classroom environment 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 attitudetowards mathematics


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-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


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APPRECIATION

Completing this project has been a most wonderful and enjoyable experience. In

doing so, I have learnt a great many things about index numbers, price comparison,

graphical representations and price index. Firstly, I would like to thank my Additional

Mathematics teacher, Mr. Azmi Nazar for his guidance and also giving me useful and

important information to complete this project work. Besides, I would like to thank my

parents for their support and encouragement. Last but not least, a big THANK YOU too to all

my friends for their help and cooperation in searching for information to complete this

project work.


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A BRIEF HISTORY OF STATISTICS

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 allthe 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 ps ychology

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 predictions, st atistics has great overlap with the decision science and

microeconomics. With its concerns with data, statistics has overlap with information science

and computer science.


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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 itsorigins. 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.


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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.

QUESTION

a) Collect pictures, newspaper cuttings or photos on items t hat you have chosen. Design a

collage to illustrate the chosen items

Answer:


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(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)

Shop A Shop B Shop C

Food 1. Self-Raising Flour (1000g) 3.70 3.60 3.99

2. Sugar (1000g) 1.65 1.65 1.65

3. Butter (250g) 4.10 4.50 4.30

4. Eggs(Grade A) 0.32 0.33 0.35

Total Price 9.77 10.08 10.29

Detergent 1. Liquid Detergent 12.90 12.95 12.99

2. Floor Cleaner 8.90 9.00 8.99

3. Clothes Softener 6.80 6.89 6.99

4.Powder Detergent 13.90 10.99 13.99Total Price 42.50 39.83 42.96

Stationery 1. Ballpoint Pen 1.60 1.50 1.70

2. Liquid Paper 3.70 3.60 3.99

3. Ruler 0.45 0.50 0.50

4. Eraser 1.30 1.00 1.30

Total Price 7.05 6.60 7.49

Grand Total 59.32 56.51 60.74


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(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:

Food

Detergent

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


Self-Raising Flour (1000g)

Sugar (1000g)

Butter (250g)

Eggs(Grade A)

0

2

4

6

8

10

12

14

16


Liquid Detergent

Floor Cleaner

Clothes SoftenerPowder Detergent


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Stationary

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Ballpoint Pen

Liquid Paper

uler

Eraser


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(d) B

sed on the graphical representation that you haveconstructed in Part 1(c),interpret,

discuss and draw conclusions

Comment on your findings

Answer:

Based on the graphical representation that I haveconstructed in Part 1(c), it isshown that

there are large and small differences among the pries of items in each category between the

shops

In the food category, thesmallest pricedifferences areeggs, while the highest is the price of

butter. Sugar is a controlled item so the price in all threesupermarkets are thesame which

is RM 1.65 per kilo. Besides food, detergent also shows a large price difference between its

items. Among them are the price ofclothessoftener and powder detergent. On the other

hand, stationery items dont have any obvious pricedifference. The graph also show that

most of the items that are high priced comes fromShop C, while the lowest price items

come from theShop B. The graph 1(d) will show theconclusion of the difference among the

shops based upon theshops grand total.

Graph 1(d)

54

55

56

57

58

59

60

61

Grand Total

Shop A

ShopB

Shop C


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(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:

Powder Detergent

Mean,=

=12.96

Standard deviation

= /N -

=

=1.393

Based on my research, I found out that Shop A sold this product for RM 13.90, Shop B for

RM 10.99 and Shop C RM 13.99. Shop B obviously has the lowest price. The reason for the

price difference could be because Shop B is currently having a Mega Sale or are trying to

clear old stock to bring in new ones. Besides, Shop B could be having promotions for this

item and are giving out free samples along with t he item where else Shop A and Shop C are

selling at standard price.


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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 b utter cakes, your class has

decided to carry out the same project for this years 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 reasons for purchasing from the shop you suggested.

Answer:

Shop A. This is because the total price of the ingredients for baking the butter cakes from

this shop is the lowest among the three shops. Therefore I can save a lot from buying the

ingredients.

(b) Complete Table 2 with the prices of the items found in the Shop/supermarket that you

have chosen

Answer:

Ingredient Quantity per cake Price in the year

2009 (RM)

Price in the year

2010 (RM)

Self-raising flour 250g 0.90 0.93

Sugar 200g 0.35 0.33

Butter 250g 3.30 4.10

Eggs (Grade A) 5 eggs (300g) 1.25 1.60

Table 2


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(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)

Price in the

year

2010 (RM)

Price index for the

year 2010 based on the

year 2009 (I)

Self-raising

flour

250g 0.90 0.93 103.33

Sugar 200g 0.35 0.33 94.29

Butter 250g 3.30 4.10 124.24

Eggs (Grade A) 5 eggs

(300g)

1.25 1.60 128.00

1.Self-Raising Flour

I = x 100

=103.33

2.Sugar

I = x 100

=94.29

3.Butter

I = x 100

=124.24

4.Eggs (Grade A)

I = x 100

=128.00


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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), Weight/Total weight

Ingredient Weightage (W)

Self-Raising Flour 250 1000 = 0.25

Sugar 200 1000 = 0.20

Butter 250 1000 = 0.25

Eggs (Grade A) 300 1000 = 0.30

Composite Index

=

=

= 114.15

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

Answer:

In 2009, RM 15.00

In 2010, price is

x 100 =114.15 % x 100 = 114.15 x 15

=

= 17.12

Thus, the suitable price for the butter cake for the year 2010 is RM 17.12 .The increase in

price is also suitable because of the rise in the price of the ingredients.


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(c)

(i)Find out from reliable source 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 750Watts of electrical power. It is suitable for a room size 1000ft which is

around 27m of volume.

(ii)Work in group 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:

After discussions and some measurements, my friends and I have come to the conclusion

that the volume of our school is 11,550 cubic feet [ 30ft X 35 ft X 18ft] or 311.85 311.9m

[9m X10.5m X 5.5m]. This measurement was achieved by counting the number of 3x3 ft

asbestos ceiling in our school library. The height of the library is the standardized 11 feet.

When choosing an air conditioner, usually a 1HP [horse power] equipment can reduce 9,000

BTU/hr of heat. The cooling capacity of an air conditioning system is expressed in BTUs or

tons. One ton of cooling capacity equals 12,000 BTUs/hour of cooling capacity and also

referring to the cooling capacity of a ton of ice. The number of air conditioner needed for

the school library:

For 311.9 m= = 11.6 12

This means our school library needs approximately 12 units of air conditioner.


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(iii)If your class intends to sponsor one air conditioner for the School library, how many

butter cakes must you sell in order to buy the air conditioner

Answer:

The cost for 1 unit of 1HP air conditioner = RM1270

Cost for a cake = 0.93 + 0.33 + 4.1 + 1.6

= RM 6.96

Selling price = RM17.12

Profit = 17.12 -6.96

= RM 10.16

Number of cakes to be sold to buy 1 unit of air conditioner =

= 125


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PART 3

As a committee member for the carnival, you are required to prepare an estimated budget

to organize this years carnival. The committee has to take into the consideration the

increase in expenditure from the previous year due to inflation. The price of foo d,

transportation and tents has increased by 15%. The cost of games, prizes a nd decorationsremains 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 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


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(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.

Answer:

Expenditure Amount in

2009(RM)

Amount in

2010(RM)

Price

Index, I

Weightage,

W

Food 1200.00 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

=

= =

= 111.625

The total price for the year 2009 is RM4000 while the total price for the year 2010 is

RM4465. The total price for the year 2010 has increased by 11.625%.This is because some

items have increased in price in the year 2010.


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(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.

Answer:

Composite index for the year 2009 to the year 2010=111.625

Composite index for the year 2010 to the year 2011= 111.625

x 100 = I x I

I = 111.625 x 111.625 x

I

= 124.60


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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 choice. Elaborate the use and the importance of

these index numbers in daily life.


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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 numbers of your choice. Elaborate the use and the importanceof this index number in daily life.

Air Pollution Index

Air pollution is the introduction of chemicals, particulate matter, or biological materials that

cause harm or discomfort to human 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 Earths 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 given location. As the AQI increased, an increasingly large percentage of the

population is l ikely 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 colour 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 level are high.

Limitation 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 d ioxide 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 are 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.


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Indices by Location

South Korea

The Ministry of Environment of South Korea uses the Comprehensive 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 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 Implication

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 meagre impact on patients

in case of chronic exposure101 150 Unhealthy for sensitive

group

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 sensitive groups and haveharmful 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 indexs

pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulphur 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 closed. There may

also be a prohibition on private sector commercial and industrial activities in the reporting

area excluding the food sector.

*An AQI of PM10 corresponds to a PM10 level of 150 micrograms per cubic meter (averaged

over 24 hours)

Index Values* Levels of Health

Concern

Cautionary Statement

0 50 Good None

51 100 Moderate None

101 150 Unhealthy for

sensitive groups

People with respiratory diseases such as asthma,

should limit outdoor exertion

151 200 Unhealthy People with respiratory diseases such as asthma,

should limit outdoor exertion; everyone else,

especially the elderly and children, should limit

prolonged outdoor exertion

201 300 Very unhealthy People with respiratory diseases such as asthma,

should limit outdoor exertion; everyone else,

especially the elderly and children, should limitprolonged outdoor exertion

301 500 Hazardous Everyone should avoid any outdoor exertion; people

with respiratory disease, such as asthma, should

remain indoors


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Stock Market Index

There are a number of interesting observations that one can make from this graph:

The MACD indicator (bottom section of graph) has just given a sell signal

as evidenced by the blue histogram bars falling below the zero line. These

signals do not occur often the last one, a buy signal, was given in May

2003 and the sell signal before that happened in Sep tember 1999.

The more sensitive RSI (internal relative strength) oscillator (top section of

graph) has fallen below 70, thereby giving its first sell signal since 1998. (A

buy signal was registered four years later in 2002.)

The 20- and 40-month moving averages (middle section of graph) are still

intact, but these are lagging indicators and the turning down and crossing

over of the two lines typically only serve as final confirmation of turningpoints in the index.

A stock market index is a method of measuring a section of the stock market. Many indices

are cited by news of 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

nations largest stock exchanges such as the American S&P500, the Japanese Nikkei 225 and

the British FTSE 100.

The concept many be extended well beyond an exchange. The Dow Jones Total Stock

Market Index as its name implies represents the sticks 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. These versions can differ based

on how the index components are weighed 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 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 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 weighed.


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Uses and importance of air pollution index and stock market index

As everyone can see, the air pollution index is used by the government to measure

the air quality index and to detect any pollutants in our countrys air. This is to ensure the air

is clean and safe for us to inhale. Besides, an early warning can be given to us if the air

pollution is too high for us to get out of our homes. This warning is given based uponreadings and interpretations of the air pollution index.

As for stock market index, it is mainly for the business entrepreneurs. 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 important because a countrys economical state

sometimes depend on it.


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Conclusion

After doing some researches, answering questions, drawing graphs and some

problem solving, I realize that the usage of statistics is very important in our 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. It is used especially in conducting air-pollution or water-pollutionsurveys. In conclusion, statistics is a daily life necessity. Without it, surveys cannot be

conducted, the stock market cannot be interpreted and many more. So, we should be

thankful to the people who contributed in the idea of statistics.


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REFLEC

N

After spending countless hours, days and night to finish this project and also sacrificing my

time in this midyear holiday, there areseveral things that I want to say

In the process of completing this project, it makes me realize how important Additional

Mathematics is to everydays life. In addition, completing this project makes me realize how

fun it is and likable is Additional Mathematics. To those who still dont really like thissubject,

you must takeyour first step to love it. You must make it likeyour friend. Then you will also

realize how important it is in your life.

IADDITIONAL

MATHEMATICS

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