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
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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
Additional Mathematics Project Work 4/2010
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.
Additional Mathematics Project Work 4/2010
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.
Additional Mathematics Project Work 4/2010
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:
Additional Mathematics Project Work 4/2010
Food
Additional Mathematics Project Work 4/2010
Lllllllllllllllllllllllllllllllllllllll
Additional Mathematics Project Work 4/2010
lllllllllllllllllllllllllllllllllllllll
Additional Mathematics Project Work 4/2010
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
Additional Mathematics Project Work 4/2010
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)
Additional Mathematics Project Work 4/2010
2)
Additional Mathematics Project Work 4/2010
3)
Additional Mathematics Project Work 4/2010
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)
Additional Mathematics Project Work 4/2010
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
Additional Mathematics Project Work 4/2010
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
Additional Mathematics Project Work 4/2010
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
Additional Mathematics Project Work 4/2010
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.
Additional Mathematics Project Work 4/2010
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.
Additional Mathematics Project Work 4/2010
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
Additional Mathematics Project Work 4/2010
Question
b) Calculate the composite index for the estimated budget of the carnival in the year 2010 based on