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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
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CONTENT
Introduction ______________________________
Objectives ______________________________
Appreciation ______________________________
Part 1 ______________________________
Part 2 ______________________________
Part 3 ______________________________
Further Exploration ______________________________
Conclusion ______________________________
Reflection ______________________________
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History of statistic
By the 18th century, the term "statistics" designated the systematic
collection of demographic and economic data by states. In the early 19th century, the
meaning of "statistics" broadened, then including the discipline concerned with 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.
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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 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.
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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.
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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.
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Part 1
The prices of goods sold in shops vary from one shop to another.
Shoppers tend to buy goods which are not only reasonably priced but
also give value for their money.
You are required to carry out a survey on four different items based
on the following categories i.e. food, detergent and stationery. The
survey should be done in three different shops.
a)Collect pictures, newspaper cuttings or photos on items that youhave chosen. Design a collage to illustrate the chosen items
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Answer:
Food
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Question :
(b) Record the items and their prices systematically as in Table
1.Since items maybe differently packed,be sure to use consistent
measurements for each item selected so that comparison can be done
easily and accurately.
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
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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
The Store C-Mart Tesco
Self-raising flour
Sugar
Butter
Eggs(Grade A)
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2)
0
2
4
6
8
10
12
14
16
18
20
The Store C-Mart Tesco
Soap(3 bar)
Liq
i
ishwasher(1000ml)
Toilet cleaner(500ml)
Clothes
etergent(3 kg)
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3)
0
1
2
3
4
5
6
The Store C-Mart Tesco
Sharpener
Pencil 2B(1 Dozen)
Pen
Eraser
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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
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Question :
(e) Identify an item that has a large price difference
among the shops. Calculate the mean and standard deviation of that
particular item. Hence, suggest and discuss possible reasons for the
price difference.
Answer :
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.
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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 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
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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
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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
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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.
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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
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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
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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.
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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
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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.
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.
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Limitations of the AQI
Most air contaminants do not have an associated AQI. Many
countries monitor ground-level ozone, particulates, sulphur
dioxide, carbon monoxide and nitrogen dioxide and calculate air
quality indices for these pollutants.
Causes of Poor Air Quality
The AQI can worsen (go up) due to lack of dilution of air
emissions by fresh air. Stagnant air, often caused 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.
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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.
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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.
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Types of indices
Stock market indices may be classed in many ways. A 'world' or 'global'
stock market index includes (typically large) companies without regard for
where they are domiciled or traded. Two examples are MSCI World and S&P
Global 100.
A national index represents the performance of the stock market of a given
nation and by proxy, reflects investor sentiment on the state of its economy.
The most regularly quoted market indices are national indices composed of the
stocks of large companies listed on a nation's largest stock exchanges, such as
the American S&P 500, the Japanese Nikkei 225, and the British FTSE 100.
The concept may be extended well beyond an exchange. The Dow Jones Total
Stock Market Index, as its name implies, represents the stocks of nearly every
publicly traded company in the United States, including all U.S. stocks traded
on the New York Stock Exchange (but not ADRs) and most traded on
the NASDAQ and American Stock Exchange. Russell Investment Group added
to the family of indices by launching the Russell Global Index.
More specialised indices exist tracking the performance of specific sectors of
the market. The Morgan Stanley Biotech Index, for example, consists of
36 American firms in the biotechnology industry. Other indices may track
companies of a certain size, a certain type of management, or even more
specialized criteria one index published by Linux Weekly News tracks
stocks of companies that sell products and services based on
the Linux operating environment.
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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.
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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.
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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