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PROJECT WORK FOR ADDITIONAL
MATHEMATHICS 2010
CURRICULUM DEVELOPMENT DIVISION
MINISTRY OF EDUCATION MALAYSIA
PROJECT WORK 4
STATISTICS
NAME : ABDUL MAJID BIN ABD AZIZ
CLASS : 5 SCIENCE 1
IC NUMBER : 930206-08-5689
SUBJECT TEACHER : SIR RAFHAN BIN AHMAD
SEKOLAH MENENGAH RAJA DR NAZRIN SHAH
KG GAJAH
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 this individually.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
APPRECIATION
Alhamdullilah,thank you to Allah for giving the will to me to complete
this Additional Mathematics project.Secondly, I would like to thank the
principle of Sekolah Menengah Raja Dr. Nazrin Shah, Mr. Hj. Omar Bin
Bakar A.M.P,P.P.T for giving me the permission to do my this Additional
Mathematics Project Work. I also like to thank my Additional
Mathematics teacher, Sir Rafhan for the guide and giving useful and
important information for me to complete this project work.
Besides that, I would like to thank my parents for their support and
encouragement. Lastly, a special thanks to all my friends for their help
and cooperation in searching for information and completing this
project work.
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 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.
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.
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 that you
have chosen.Design a collage to illustrate the chosen items
Answer: FOODS :
DETERGENTS :
STATIONARY :
(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)
KOOP SARJANA
KOOP IUI
KIOSK PUM
FOOD 1.SELF-RAISING FLOUR (1000 g)
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
(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)FOODS
0
1
2
3
4
5
6
KOOP SARJANA
SELF-RAISING FLOUR (1000 g)
SUGAR (1000g)
BUTTER (250g)
EGGS (GRADE A) 1 DOZEN
0
1
2
3
4
5
6
KOOP IUI
SELF-RAISING FLOUR (1000 g)
SUGAR (1000g)
BUTTER (250g)
EGGS (GRADE A) 1 DOZEN
0
1
2
3
4
5
KIOSK PUM
SELF-RAISING FLOUR (1000 g)
SUGAR (1000g)
BUTTER (250g)
EGGS (GRADE A) 1 DOZEN
2)DETERGENT
0
5
10
15
20
KOOP SARJANA
SOAP (3 BARS)
LIQUID DISHWASHER (1000ml)
CLOTHES DETERGENT (3KG)
TOILET CLEANER (500ml)
0
2
4
6
8
10
12
14
16
18
KOOP IUI
SOAP (3 BARS)
LIQUID DISHWASHER (1000ml)
CLOTHES DETERGENT (3KG)
TOILET CLEANER (500ml)
0
2
4
6
8
10
12
14
16
18
KIOSK PUM
SOAP (3 BARS)
LIQUID DISHWASHER (1000ml)
CLOTHES DETERGENT (3KG)
TOILET CLEANER (500ml)
3)STATIONERY
0
1
2
3
4
5
KOOP SARJANA
SHARPENER
PENCIL (2B) 1 DOZEN
PEN
ERASER
0
1
2
3
4
5
KOOP IUI
SHARPENER
PENCIL (2B) 1 DOZEN
PEN
ERASER
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
KIOSK PUM
SHARPENER
PENCIL (2B) 1 DOZEN
PEN
ERASER
(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 representation that I have constructed
in Part 1(c), it is shown that there are large and small
differences among the pries of items in each category between
the shops.In the food category, the smallest price difference
are of those 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 KOOP SARJANA, while the lowest price items
come frm the KIOSK PUM.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
GRAND TOTAL
KOOP SARJANA
KOOP IUI
KIOSK PUM
(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
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.
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 Giant Supermarket.This is because the total price of the
ingredients from this shop is the lowest from the three shops.
(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 0.90
Sugar 200g 0.35 0.36
Butter 250g 3.30 4.30
Eggs (Grade A) 5 eggs (300g) 1.25 2.10
Table 2
(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 YEAR2010 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 x 100 = 100 2.Sugar I = 0.36
0.35 x 100 = 102.86 3.Butter I = 4.3
3.3 x 100 = 130.30 4.Eggs (Grade A) I = 2.1
1.25 x 100 = 168
(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), 𝑊𝑒𝑖𝑔 ℎ𝑡𝑇𝑜𝑡𝑎𝑙 𝑊𝑒𝑖𝑔 ℎ𝑡
INGREDIENT WEIGHTAGE (W)
Self-Raising Flour 250
1000 = 14
Sugar 2001000 =
15
Butter 2501000 =
14
Eggs (Grade A) 3301000 =
310
Composite Index =
14 (100)+
15 (102.86)+
14 (130.30)+
310(168)
1 = 128.54
(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 = 𝜘
15 x 100 = 128.54%
𝜘 x 100 = 128.54 x 15
𝜘 = 1928.1
100
𝜘 = 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.
(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 700W to 1000W
of electrical power. It is suitable for a room size 1000ft³
which is around 27m³ 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:
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 x 9.17 x 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
(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:
1 unit of 1HP air conditioner =RM700
Cost for a cake = 0.9 + 0.36 + 4.3 + 2.1
= RM 7.66
Selling price = RM19.30
Profit = 19.30 – 7.66
= RM 11.64
Number of cakes = 700
11.64
to buy 1 unit of = 60.13 air conditioner = 60 cakes
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)
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
(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 AMOUN
T IN
2009
(RM)
AMOUN
T IN
2010
(RM)
PRICE
INDEX
, I
I = 𝑃1𝑃0 X
100%
WEIGHTAG
E, W
FOOD 1200.00 1380.00 115 12
GAMES 500.00 500.00 100 5
TRANSPORTATIO
N
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
I = ∑𝐼𝑖𝑊𝑖
∑𝑊
= 115 12 +100 5 +115 3 +100 2 +100 6 +115 8 +130(4)
12+5+3+2+6+8+4
=
446540
= 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.
(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
I2011
2009 X 100 = I2010
2009 X I2011
2009
I2011
2009 = 111.625 X111.625 X
1
100
I2011
2009 = 124.60
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) 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.
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.
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/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.
STOCK MARKET INDEX
A comparison of tree major U.S. stock indices: the NASDAQ
Composite, Dow Jones Industrial Average, andS&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
nation²and 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.
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 quality of air index and to detect any pollutants in our country’s air.This is to ensure the air is clean and safe for us ti 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 unterpretations of the air 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.
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 nessecities.Without it,surveys can’t be conducted,the stock market can’t be interpret and many more.So,we should be thankful of the people who contribute in the idea of statistics.
REFLECTION Adter spending countless hours,days and night to finish this project and also sacrificing my time video games and mangas in this mid year holiday,there are several things that I can say... Additional Mathematics... From the day I born... From the day I was able to holding pencil... From the day I start learning... And... From the day I heard your name... I always thought that you will be my greatest obstacle and rival in excelling in my life... But after countless of hours... Countless of days... Countless of nights... After sacrificing my precious time just for you... Sacrificing my Computer Games... Sacrificing my Video Games... Sacrificing my Facebook... Sacrificing my Internet... Sacrifing my Anime... Sacrificing my Manga... I realized something really important in you... I really love you... You are my real friend... You my partner... You are my soulmate... I LOVE U ADDITIONAL MATHEMATICS...