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Additional Mathematics Project Work 4/2010
STATISTICS IN OUR DAILY LIFE
PROJECT WORK FOR ADDITIONAL
MATHEMATICS 2010
NAMA: MOHD KHAIRUL SYAZWAN BIN MUHAMAD
NO. KAD PENGENALAN: 930719-06-5587
GURU PEMBIMBING: PN FAIZATUL HANIS BINTI SAHIR
SEKOLAH: SEKOLAH MENENGAH SAINS TENGKU ABDULLAH
Additional Mathematics Project Work 4/2010
CONTENTNO CONTENTS
1 Introduction2 Appreciation3 Part 14 Part 25 Part 36 Further
Exploration7 Reflection
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
Additional Mathematics Project Work 4/2010
tasks for us. We are to choose and complete only ONE task based on our area of interest. This
project can be done in groups or individually, but each of us are expected to submit an individually
written report. Upon completion of the Additional Mathematics Project Work, we are to gain
valuable experiences and able to:
Apply and adapt a variety of problem solving strategies to solve routine and 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 classroom environments that stimulates and enhances effective learning.
Acquire effective mathematical communication through oral and writing, and to use the
language of mathematics to express mathematical ideas correctly and precisely
Enhance acquisition of mathematical knowledge and skills through problem-solving in
ways that increase interest and confidence
Prepare ourselves for the demand of our future undertakings and in workplace
Realise that mathematics is an important and powerful tool in solving real-life problems and
hence develop positive attitude towards mathematics.
Train ourselves not only to be independent learners but also to collaborate, to cooperate, and
to share knowledge in an engaging and healthy environment
Use technology especially the ICT appropriately and effectively
Train ourselves to appreciate the intrinsic values of mathematics and to become more
creative and innovative
Realize the importance and the beauty of mathematics
We are expected to submit the project work within three weeks from the first day the task is
being administered to us. Failure to submit the written report will result in us not receiving
certificate.
Appreciation
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Alhamdullilah, thank you to Allah for giving the will to do my additional mathematics project.
Next, I would like to thank the principle of Sekolah Menengah Sains Tengku Abdullah, Tuan Haji
Kamaruddin Bin Haji Kasim for giving the permission to do my Additional Mathematics Project
Work. I also like to thank my Additional Mathematics teacher, Puan Faizatul Hanis Binti Sahir for
the guide and giving useful and important information for me to complete this project work.
Besides, I would like to thank my parents 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.
Additional Mathematics Project Work 4/2010
History of statistic
By the 18th century, the term "statistics" designated the systematic collection of demographic and
economic data by states. In the early 19th century, the meaning of "statistics" broadened, then
including the discipline concerned with the collection, summary, and analysis of data. Today
statistics is widely employed in government, business, and all the sciences. Electronic computers
have expedited statistical computation, and have allowed statisticians to develop "computer-
intensive" methods. The term "mathematical statistics" designates the mathematical theories of
probability and statistical inference, which are used in statistical practice. The relation between
statistics and probability theory developed rather late, however. In the 19th century, statistics
increasingly used probability theory, whose initial results were found in the17th and 18th centuries,
particularly in the analysis of games of chance (gambling). By 1800, astronomy used probability
models and statistical theories, particularly the method of least squares, which was invented by
Legendre and Gauss. Early probability theory and statistics was systematized and extended by
Laplace; following Laplace, probability and statistics have been in continual development. In the
19th century, social scientists used statistical reasoning and probability models to advance the new
sciences of experimental psychology and sociology; physical scientists used statistical reasoning
and probability models to advance the new sciences of thermodynamics and statistical mechanics.
The development of statistical reasoning was closely associated with the development of inductive
logic and the scientific method. Statistics is not a field of mathematics but an autonomous
mathematical science, like computer science or operations research. Unlike mathematics, statistics
had its origins in public administration and maintains a special concern with demography and
economics. Being concerned with the scientific method and inductive logic, statistical theory has
close association with the philosophy of science; with its emphasis on learning from data and
making best 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 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.
a) Collect pictures, newspaper cuttings or photos on items that you have chosen.
Design a collage to illustrate the chosen items
Answer:
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Food
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Lllllllllllllllllllllllllllllllllllllll
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lllllllllllllllllllllllllllllllllllllll
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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 ITEMS PRICE (RM)
Mini Market Pasaraya Segar Discount Store
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-1dozen) 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 chosen.
Answer:
1)
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2)
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3)
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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 differences 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 doesn't
have any obvious price difference. The graph also show that most of the items that are high priced
comes from the B, while the lowest price items come from the Discount Store. The graph 1(d) will
show the conclusion of the difference among the shops based upon the shops grand total.
Additional Mathematics Project Work 4/2010
graph 1(d)
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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 = 18.9+17+16.5
3
=17.47
Standard deviation
=√(∑x²)/N – (x)²
=√ 18.9²+17²+16.5² - (17.47)²
3
=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.
Additional Mathematics Project Work 4/2010
Part 2
Every year SMK Indah organises a carnival to raise funds for the school. This year the school plans
to install air conditioners in the school library. Last year, during the carnival, your class made and
sold butter cakes. Because of the popularity of the butter cakes, your class has decided to carry out
the same project for this year's carnival.
Question
(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:
The Discount Store. This is because the total price of the ingredients from this shop is the
lowest from the three shops.
Question
(b) Complete Table 2 with the prices of the items found in the shop/supermarket that you
have chosen.
Answer:
Ingredient Quality Per Cake Price in the year
2009(RM)
Price in the year
2010(RM)
Self-raising flour 250g 0.90 0.90
Sugar 200g 0.35 0.36
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 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 0.90 100
Sugar 200g 0.35 0.36 102.86
Butter 250g 3.30 4.30 130.30
Eggs(Grade A) 5 eggs (300g) 1.25 2.10 168
1. Self-raising flour
I= (0.9⁄ 0.9) × 100 = 100
2. Sugar
I= (0.36/0.35) × 100 = 102.8
3. Butter
I= (4.3/3.3) × 100 = 130.30
4. Eggs (Grade A)
I= (2.1/1.25) × 100 = 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), weight/total weight
Ingredients Weightage (W)
Self-raising flour 250/1000 = 1/4
Sugar 200/1000 = 1/5
Butter 250/1000 = 1/4
Eggs (Grade A) 300/1000 = 3/10
Composite
Index = 1/4(100) + 1/5(102.86) + 1/4(130.30) + 3/10(168)
1
=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 = χ/15 × 100 = 128.54%
χ × 100 = 128.54 × 15
χ = 1928 / 100
χ = 19.30
Thus, 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.
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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 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 required 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
= 664.20m³
1 unit of air conditioner is for 27m³
For 664.20m³ = 664.20 ÷ 27
= 24.6
That means our school library needs 25 unit of air conditioner.
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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
700 / 11.64 = 60.13
= 60 cakes
Additional Mathematics Project Work 4/2010
Part 3
As a committee member for the carnival, you are required to prepare an estimated budget to
organize this year's carnival. The committee has to take into the consideration the increase in
expenditure from the previous year due to inflation. The price of food, transportation and tents has
increased by 15%. The cost of games, prizes and decorations remains the same, whereas the cost of
miscellaneous items has increase by 30%.
Question,
a) Complete Table 3 based on the information given above.
Answer ,
Expenditure Amount in 2009 (RM) Amonut in 2010 (RM)
Food 1200.00 1380.00
Games 500.00 500.00
Transportation 300.00 3450..
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 the carnival 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 = P1/P2 × 100%
Weightage , W
Food 1200.00 1380.00 115 12
Games 500.00 500.00 100 5
Transportations 300.00 345.00 115 3
Decorations 200.00 200.00 100 2
Prizes 600.00 600.00 100 6
Tents 800.00 920.00 115 8
Miscellaneous 400.00 520.00 130 4
Composite Index
Ī = ∑ IiWi
W
= 115(12) + 100(5) + 115(3) + 100(2) + 100(6) + 115(8) + 130(4)
(12 + 5 + 3 + 2 + 6 + 8 + 4)
= 4465/20
=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 for the carnival from the year 2009 to
the year 2010 is the same as the change from the year 2010 to the year 2011. Determine the
composite index of the budget for the year 2011 based on the year 2009.
Solution.
Composite index for the year 2009 to the year 2010
=111.625
Composite index for the year 2010 to the year 2011
=111.625
Ī 2011/2009 × 100 = Ī 2010/2009 × Ī 2011/2010
Ī2011/2009 = 111.625 × 1/100
Ī 2011/2009 = 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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Air Pollution Index
Air pollution is the introduction of chemicals, particulate matter, or biological materials that cause
harm or discomfort to humans or other living organisms, or damages the natural environment into
the atmosphere.
The atmosphere is a complex dynamic natural gaseous system that is essential to support life on
planet Earth. Stratospheric ozone depletion due to air pollution has long been recognized as a threat
to human health as well as to the Earth's ecosystems.
The Air Quality Index (AQI) (also known as the Air Pollution Index (API) or Pollutant
Standard Index (PSI) is a number used by government agencies to characterize the quality of the
air at a given location. As the AQI increases, an increasingly large percentage of the population is
likely to experience increasingly severe adverse health effects. To compute the AQI requires an air
pollutant concentration from a monitor or model. The function used to convert from air pollutant
concentration to AQI varies by pollutant, and is different in different countries. Air quality index
values are divided into ranges, and each range is assigned a descriptor and a color code.
Standardized public health advisories are associated with each AQI range. An agency might also
encourage members of the public to take public transportation or work from home when AQI levels
are high.
Limitations of the AQI
Most air contaminants do not have an associated AQI. Many countries monitor ground-level ozone,
particulates, sulphur dioxide, carbon monoxide and nitrogen dioxide and calculate air quality
indices for these pollutants.
Causes of Poor Air Quality
The AQI can worsen (go up) due to lack of dilution of air emissions by fresh air. Stagnant air, often
caused by an anticyclone or temperature inversion, or other lack of winds lets air pollution remain
in a local area.
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Indices by location
South Korea
The Ministry of Environment of South Korea uses the Comprehensice Air-quality Index (CAI) to
describe the ambient air quality based on health risk of air pollution. The index aims to help the
public easily understand air quality level and protect the health of people from air pollution. - The
CAI has values of 0 through 500, which are divided into six categories. The higher the CAI value,
the greater the level of air pollution. - Of values of the five air pollutants, the highest is the CAI
value.
CAI Description Health Implications
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 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-
350
Very unhealthy A level which may have a serious impact on patients and members of
sensitive groups in case of acute exposure.
351-
350
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.
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Malaysia
The air quality in Malaysia is reported as the API or Air Pollution Index. Four of the index's
pollutant components (i.e., carbon monoxide, ozone, nitrogen dioxide and sulfur dioxide) are
reported in PM10 particulate matter is reported in μg/m³.
Unlike the American AQI, the index number can exceed 500. Above 500, a state of emergency is
declared in the reporting area. Usually, this means that non-essential government services are
suspended, and all ports in the affected area closed. There may also be a prohibition on private
sector commercial and industrial activities in the reporting area excluding the food sector.
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Stock market index
A comparison of three major U.S. stock indices: the NASDAQ Composite, Dow Jones Industrial
Average, and S&P 500. All three have the same height at March 2007. Notice the large-dot com
spike on the NASDAQ, a result of the large number of tech. companies on that index.
A stock market index is a method of measuring a section of the stock market. Many indices are
cited by news or financial services firms and are used as benchmarks, to measure the performance
of portfolios such as mutual funds.
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.
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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 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.
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Uses and importance of air pollution index and stock market index
As everyone can see, the air pollution index is use by the government to measure the air quality
index and to detect any pollutants in our country's air. This is to ensure the air is clean and safe for
us to inhale. Besides that, an early warning can be given to us if the air pollution is too 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 country's 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 in markets but also in
interpreting the condition of the surrounding like the air or the water. Especially in conducting an
air-pollution survey. In conclusion, statistics is a daily life necessities. 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.
Additional Mathematics Project Work 4/2010
Reflection
While I was conducting the project, I had learned many moral values that I practice. This project
work had taught me to be more confident when doing something especially the homework given by
the teacher. I also learned to be a disciplined type of student which is always sharp on time while
doing some work, complete the work by myself and researching the information from the internet. I
also felt very enjoy when making this project during the school holidays