addm3 projek

8/9/2019 addm3 projek

1/32

Statistics In Our Daily Life

PROJECT WORK FOR ADDITIONALMATHEMATHICS 2010

Nama: Wan Muzaffar Bin Wan Muda

Guru Pembimbing: Tuan Haji Ismadi Bin Ismail

Sekolah Menengah Kebangsaan Agama Arau


2/32

CONTENT

Introduction ______________________________

Objectives ______________________________

Appreciation ______________________________

Part 1 ______________________________

Part 2 ______________________________

Part 3 ______________________________

Further Exploration ______________________________

Conclusion ______________________________

Reflection ______________________________


3/32

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 thecollection, 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 probabilitymodels 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 scientificmethod 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.


4/32

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


5/32

Objectives

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 areexpected to submit an individually written report. Upon completion of the Additional

Mathematics Project Work, we are to gain valuable 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 andmeaningful and hence improve their thinking skills.

y Experience classroom environments where knowledge and skills are applied inmeaningful ways in solving real-life problems

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

y Experience classroom environments that stimulates and enhances effective learning.y Acquire effective mathematical communication 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-solvingin ways that increase interest and confidence

y Prepare ourselves for the demand of our future undertakings and in workplacey 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, tocooperate, and to share knowledge in an engaging and healthy environment

y Use technology especially the ICT appropriately and effectivelyy Train ourselves to appreciate the intrinsic values of mathematics and to become

more creative and innovative

y Realize the importance and the beauty of mathematicsWe 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.


6/32

Appreciation

Alhamdulillah, thank you to Allah for giving the will to

do my additional mathematics project. Secondly, I would liketo thank the principle, Puan Hajjah Salmiah Sabran for giving

the permission to do my Additional Mathematics Project

Work. I also like to thank my Additional Mathematics

teacher, Tuan Haji Ismadi b. Ismail for the guide and giving

useful and important information for me to complete thisproject work. Besides that, I would like to thank my father,

Wan Muda b Wan Yahaya and my mother, Wan Kamariah bt

Wan Abd Rahman for their support and encouragement.

Lastly, a special thanks to all my friends for their help and

cooperation in searching for information and completing this

project work.


7/32

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 youhave chosen. Design a collage to illustrate the chosen items


8/32

Answer:

Food


9/32


10/32


11/32

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)

The Store C-Mart Tesco

Food

1.Self-Raising

Flour(1000g)

4.00 3.70 3.60

2.Sugar(1000g) 2.00 1.90 1.80

3.Butter(250g) 4.70 4.50 4.30

4.Eggs(Grade A)

1 dozen

5.90 5.50 5.00

Total Price 16.60 15.60 14.70

Detergent

1.Soap(3 bars) 3.20 3.00 2.80

2.Liquid

dishwasher(1000ml)

4.29 3.90 3.20

3.Clothes detergent(3kg) 18.90 17.00 16.50

4.Toilet cleaner(500ml) 5.50 5.50 5.50

Total Price 31.89 29.40 28.00

Stationery

1.Sharpener 1.50 1.30 1.00

2.Pencil

(2B-1 dozen)

5.00 4.80 4.50

3.Pen 1.30 1.20 1.00

4.Eraser 1.30 1.20 1.10

Total Price 9.10 8.50 7.60

Grand Total 57.59 53.50 50.30


12/32

Question :

(c) Create at least two suitable graphical representations (the use of

ICT is encouraged) to compare and contrast the price of the items

choosen.

Answer :

1)

0

1

2

3

4

5

6

7


Self-raising flour

Sugar

Butter

Eggs(Grade A)


13/32

2)

0

2

4

6

8

10

12

14

16

18

20


Soap(3 bar)

Liq

i

ishwasher(1000ml)

Toilet cleaner(500ml)

Clothes

etergent(3 kg)


14/32

3)

0

1

2

3

4

5

6


Sharpener

Pencil 2B(1 Dozen)

Pen

Eraser


15/32

Question :

(d) Based on the graphical representation that you have constructed in Part 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 of items 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. Besides food, detergent also shows a large price difference

between its items. Among them is the price of liquid dishwasher and clothes detergent. On

the other hand,stationery items doesnt have any obvious price difference. The graph also

show that most of the items that are high priced comes from the The Store, while the lowest

price items come from the Tesco.The graph 1(d) will show the conclusion of the difference

among the shops based upon the shops grand total.

Graph 1(d)

46

48

50

52

54

56

58

60

Grand total

T e Store

C-Mart

Tesco


16/32

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

= ()/N ( )

=

- (17.47)

=0.97

The large price difference of clothes detergent among the shops

maybe because of the standard of the shop. A high standard shop or

supermarket, the items sold intend to be much more expensive than a

regular shop or supermarket. Also, the price difference of the items

may also due to the quality of the item present. A better quality means

a higher price.


17/32

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 years carnival.

Question :

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

purchasing from the shop you suggested.

Answer :

Tesco.This is because the total price of the ingredients from this shop is the lowest

from the three shops.

Question :

Complete Table 2 with the prices of the items found in the shop/supermarket that youhave chosen.

Answer :

Ingredient Quantity

Per cake

Price in the year

2009(RM)

Price in the year

2010(RM)

Self-raising flour 250g 0.90 0.90Sugar 200g 0.35 0.36

Butter 250g 3.30 4.30

Eggs(Grade A) 5 eggs (300g) 1.25 2.10


18/32

Question :

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

Answer :

1.Self-raising flour

=

2.Sugar

=

3.Butter

=

4.Eggs(Grade 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 ()

Self-raising

flour

250g 0.90 0.90 100

Sugar 200g 0.35 0.36 102.86

Butter 250g 3.30 4.30 130.30Eggs(Grade

A)

5 eggs

(300g)

1.25 2.10 168


19/32

Question :

(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),

Ingredients Weightage (W)Self-raising flour

Sugar

Butter

Eggs(Grade A)

Composite index

=128.54


20/32

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), which is

approximately 700W to 1000W of electrical power. It is suitable for a room size 1000ft

which is around 27mof 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.


21/32

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=3.69.1720.12

=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


22/32

Part 3

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

an estiated 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 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 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


23/32

Question :

b)Calculate the composite index for the estimated budget of thecarnival 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=

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 2010 increase by 11.625%. This is because

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


24/32

Question :

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

=

=111.625111.625

124.60


25/32

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.

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) orPollutant

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.


26/32

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 byan 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 ComprehensiceAir-quality Index (CAI) to describe the ambient air quality based onhealth risk of air pollution. The index aims to help the public easilyunderstand air quality level and protect the health of people from airpollution. - The CAI has values of 0 through 500, which are divided

into six categories. The higher the CAI value, the greater the level ofair pollution. - Of values of the five air pollutants, the highest is theCAI value.


27/32

CAI Description Health Implications

0-50 Good A level that will not impact patients suffering from diseases related to air pollution.

51-

100Moderate 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-

350Very unhealthy

A level which may have a serious impact on patients and members of sensitive

groups in case of acute exposure.

351-

500Hazardous

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 g/m.

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.


28/32

St M t Index

A compari on oft ree major U.S. stockindices:t eNASDAQ Composite, Dow Jones

Industrial Average, andS&P 500. Allt ree have the same height atMarch 2007. Notice thelarge dot com spike on the NASDAQ, a result ofthe large number oftech. companies on that

index.

A stock market i exis a method of measuring a section ofthe 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.


29/32

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.


30/32

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 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 countrys

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 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.


31/32

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 inmarkets 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 cant be conducted,the stock

market cant be interpret and many more. So, we should bethankful of the people who contribute in the idea of statistics.


32/32

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 Additional

Mathematics

addm3 projek

Documents

Transcript of addm3 projek