Add Math 4

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


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


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


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.


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.


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.

a) Collect pictures, newspaper cuttings or photos on items that you have chosen.

Design a collage to illustrate the chosen items

Answer:


Food


Lllllllllllllllllllllllllllllllllllllll


lllllllllllllllllllllllllllllllllllllll


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


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)


2)


3)


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.


graph 1(d)


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.


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


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


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


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.


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.


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


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


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.


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


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.

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.


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.


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.


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.


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.


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.


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

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