add maths folio form 5

ADDITIONAL MATHEMATICS FOLIO 2010

STATISTICS IN OUR LIFE

NAME : Luqman Naim b. Mohd Esa

SCHOOL : SMK Bukit Rahman Putra

1 STATISTICS IN LIFE

No. TITLE PAGE 1. Acknowledgement 3

2. Introduction 43. History of Statistic 54. Part 1 6-115. Part 2 12-176. Part 3 18-217. Further Exploration 22-258. Conclusion 26-27


ACKNOWLEDGEMENT

First and foremost, I would like to thank my Additional Mathematics’ teacher, Puan Siti Aini bt. Jamil as she gives us important guidance and commitment during this project work. She has been a very supportive figure throughout the whole project.

I also would like to give thanks to all my friends for helping me and always supporting me to help complete this project work. They have done a great job at surveying various shops and sharing information with other people including me. Without them this project would never have had its conclusion.

For their strong support, I would like to express my gratitude to my beloved parents. Also for supplying the equipments and money needed for the resources to complete this project. They have always been by my side and i hope they will still be there in the future.

Last but not least, i would also like to thank all the nice shopkeepers, staffs, and citizens for helping me collect the much needed data and statistics for this. Not forgetting too all the other people who were involved directly or indirectly towards making this project a reality.

I thank you all.


INTRODUCTION

This project is carried out by every student who taking Additional Mathematic in their SPM examination. This project carries such aims:-

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.

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.


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.

COLLAGE


Item Price (RM)Shop A Shop B Shop C

FOOD1. Self-Raising Flour (250g) 1.15 1.10 1.00

2. Sugar (1kg) 1.60 1.60 1.60

3. Butter (250g) 3.99 3.60 3.42

4. Grade “A” Eggs (5 eggs) 2.25 1.66 1.55

Total Price 0 8.99 7.96

DETERGENT (1kg)

1. Breeze 5.25 4.99 4.80

2. Bio Zip 3.70 3.70 3.60

3. Softlan 3.50 3.15 3.20

4. TOP 5.60 4.39 4.50

Total Price 18.50 16.23 16.10

STATIONERY(1pc)

1. Stabilo Eraser 1.60 1.15 1.20

2. Stabilo Sharpener 2.50 2.50 2.50

3. Stabilo Highlighter 3.90 3.90 3.90

4. Whiteboard Marker 2.00 2.00 2.00

Total Price 10.00 9.55 9.60

Grand Total 37.49 33.74 33.27

TABLE


GRAPHICAL PRESENTATION

1) Bar Chart

Shop A Shop B Shop C0

1

2

3

4

5

6

Raising FlourSugarButterEggsBreezeBio ZipSoftlanTopStabilo EraserStabilo SharpenerStabilo HighlighterWhiteboard Marker

2)Line Graph


Shop A Shop B Shop C0

1

2

3

4

5

6

Raising Flour

Sugar

Butter

Eggs

Breeze

Bio Zip

Softlan

Top

Stabilo Eraser

Stabilo Sharpener

Stabilo Highlighter

Whiteboard Marker

INTERPERTRATION & DISCUSSION

Based on the survey from three shops above, we can conclude that the shop which is selling the products with higher price is shop A. But we can say that all the products are expensive in this shop because certain products from the shop is reasonable than the other shops such as Softlan detergent and eraser. The survey also says that the shop B sells the most reasonable products among the three shops. The cheapest product in the survey is the Self-Raising Flour in shop C while the most expensive product is the TOP detergent in shop A.

IDENTIFICATION & CALCULATION

The item that has the largest price difference among the shops is the Grade “A” Eggs.

Mean

Step 1: Find the sum of the numbers. RM 2.25+ RM 1.66+ RM 1.55 = RM 5.46

Step 2: Calculate the total number. there are 3 numbers.


Step 3: Finding mean. RM 5.46/3= RM 1.82

Standard Deviation

S=√∑(X−M )2

N−1

Where Σ = Sum of X = Individual score M = Mean of all scores N = Sample size (Number of scores)

X M (X-M) (X-M)2

2.25 1.82 0.43 0.18491.66 1.82 -0.16 0.02561.55 1.82 -0.27 0.0729

STEP 1: Find the sum of (x-m) 2

0.1849 + 0.0256 + 0.0729 = 0.2834


Step 2: find n-1

3-1= 2

Step 3: find the standard deviation using formula

√0.2834/2 = 0.37643


Every year SMK Bukit Rahman Putra 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.

Self-Raising Flour

I = 1.00/0.90 × 100

= 111.111

Sugar

I = 0.32/0.35 × 100

= 91.429

Butter

I = 3.42/3.30 × 100

= 103.636

SUGGESTION & DISCUSSION

I would go and purchase the ingredients for the butter cakes from shop C. This is because the total price for the ingredients needed for making butter cakes in shop C is the cheapest amongst the three shops.

Table 2

Ingredient Quantity percake

Price in the year 2009 (RM)

Price in the year 2010 (RM)

Self-raising flour 250 g 0.90 1.00Sugar 200g 0.35 0.32Butter 250g 3.30 3.42Eggs (Grade A) 5 eggs (300g) 1.25 1.15

Price Index for each ingredients

I = Price index/ Index number

P0 = Price at the base time


I = P1/P0 × 100

Self-Raising Flour

I = 1.00/0.90 × 100

= 111.111

Sugar

I = 0.32/0.35 × 100

= 91.429

Butter

I = 3.42/3.30 × 100

= 103.636

P1 = Price at a specific time

Composite index for making a butter cake

Ī = Composite Index

W = Weightage

I = Price Index

Items I WSelf-Raising Flour 111.111 2.5

Sugar 91.429 2.0

Butter 103.636 2.5

Eggs (Grade A) 92 3.0

Ī = 111.111(2.5)+ 91.429 (2.0)+ 103.636 (2.5)+ 92 (3.0)

2.5+2.0+2.5+3.0

Ī = 99.573


I=∑W 1 I 1

∑W 1

Suitable selling price for butter cake in the year 2010

In the year 2010 the butter cake is suitable to sell for :

= RM 15.00 × 99.573 / 100

= RM 14.94

= RM 15.00

The suitable price would be RM 15.00 per butter cake, which is the same as the year 2009. This is because the price index has lowered in 2010 based on 2009.

RELIABLE SOURCES IN DETERMINING SUITABLE AIR-CONDITIONER CAPACITY TO BE INSTALLED

Properly Sized Room Air Conditioners

Many people buy an air conditioner that is too large, thinking it will provide better cooling. However, an oversized air conditioner is actually less effective — and wastes energy at the same time. Air conditioners remove both heat and humidity from the air. If the unit is too large, it will cool the room quickly, but only remove some of the humidity. This leaves the room with a damp, clammy feeling. A properly sized unit will remove humidity effectively as it cools.

To figure out which size unit is best for your cooling needs:

1. Determine the square footage of the area to be cooled using the following formulas:o For square and rectangular rooms, multiply the length of the area by its widtho For a triangular area, multiply the length of the area by the width and divide

by 2

Most rooms can be further divided into these basic shapes to determine the square footage.

If the shape of your room is other than square or rectangular, ask your sales associate to help you determine the square footage.


2. Using the square footage and the chart below, determine the correct cooling capacity. Cooling capacity is measured in British Thermal Units (BTUs) per hour.

Area To Be Cooled (square feet) Capacity Needed (BTUs per hour) 100 to 150 5,000151 to 250 6,000251 to 300 7,000301 to 350 8,000351 to 400 9,000401 to 450 10,000451 to 550 12,000551 to 700 14,000701 to 1,000 18,0001,001 to 1,200 21,0001,201 to 1,400 23,0001,401 to 1,500 24,0001,501 to 2,000 30,0002,001 to 2,500 34,000

3. Make any adjustments for the following circumstances:o If the room is heavily shaded, reduce capacity by 10 percent.o If the room is very sunny, increase capacity by 10 percent.o If more than two people regularly occupy the room, add 600 BTUs for each

additional person.o If the unit is used in a kitchen, increase capacity by 4,000 BTUs.o Consider where you install the unit. If you are mounting an air conditioner

near the corner of a room, look for a unit that can send the airflow in the right direction.


NUMBER OF AIR-CONDITIONERS WITH THE APPROPIATE CAPACITY REQUIRED FOR LIBRARY

The height, length and width of the school library was measured using a measuring tape.

HEIGHT = 4.3 meters

LENGTH = 20.8 meters

WIDTH = 9.27 meters

Thus the volume of our school library is :

4.3m × 20.8m × 9.27m = 829.109m3

From the information given : Area = Height × Width

Area of school library = 4.3m x 9.27m = 39.86m2

1 m2 = 10.8 square feet (sf)

39.86m2 = 430.5sf

The amount of (BTU’s per hour) needed to cool down 450sf of area is 10,000. Therefore, 5 air-conditioners with 2000 BTU’s each are needed to cool down the school library.

NUMBER OF BUTTER CAKES THAT HAVE TO BE SOLD IN ORDER TO BUY ONE AIR-CONDITIONER

1 Air-conditioner = RM 900

Cost of 1 butter cake = RM 15


Volume = Height × Length × Width

Income earned from 1 butter cakes = RM 10.00

Selling price = RM 25.00

Number of butter cakes that have to be sold : 900/10.00

: 90 cakes


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%.

Table EXPENDITURE AMOUNT IN 2009

(RM)AMOUNT IN 2010

(RM)Food 1200.00 1380.00

Games 500.00 500.00Transportation 300.00 345.00

Decorations 200.00 200.00Prizes 600.00 600.00Tents 800.00 920.00

Miscellaneous 400.00 520.00

Amount in 2010 :

Food: 1200.00 + 15℅ = RM 1380.00

Games : RM 500.00

Transportation: 300.00 + 15℅ = RM 345.00

Decorations: RM 200.00

Prizes: RM 600.00

Tents: 800.00 + 15℅ = RM 920.00

Miscellaneous: 400.00 + 30℅ = RM 520.00


COMPOSITE INDEX FOR THE BUDGET IN THE YEAR 2010 BASED ON THE YEAR 2009

EXPENDITURES Index (I) Weightage (W)

Food 115 15Games 100 0Transportation 115 15Decorations 100 0Prizes 100 0Tents 115 15Miscellaneous 130 30

I for Food = 1380/1200 × 100 = 115

I for Games = 5000/500 × 100 = 100

I for Transportation = 345/300 × 100 = 115

I for Decorations = 200/200 × 100 = 100

I for Prizes = 600/600 × 100 = 100

I for Tents = 920/800 × 100 = 115

I for Miscellaneous = 130

Ī = 115(15) + 100(0) + 115(15) + 100(0) + 100(0) + 115(15) + 130(30)

15+15+15+30


Ī = 121

The budget for the carnival has increased as much 21 ℅ in the year 2010 compared to the year 2009.

COMPOSITE INDEX OF THE BUDGET FOR THE YEAR 2011 BASED ON 2009

EXPENDITURES PRICE IN 2009 PRICE IN 2010 PRICE IN 2011

Food 1200.00 1380.00 1587.00Games 500.00 500.00 500.00Transportation 300.00 345.00 396.75Decorations 200.00 200.00 200.00Prizes 600.00 600.00 600.00Tents 800.00 920.00 1058.00Miscellaneous 400.00 520.00 676.00

EXPENDITURES Index (I) Weightage (W)

Food 132.25 15Games 100.00 0Transportation 132.25 15Decorations 100.00 0Prizes 100.00 0Tents 132.25 15Miscellaneous 169.00 30

I for Food = 1587.00/1200.00 × 100 = 132.25

I for Games = 500.00/500.00 × 100 = 100

I for Transportation = 396.75/300.00 × 100 = 132.25

I for Decorations = 200.00/200.00 × 100 = 100

I for Prizes = 600.00/600.00 × 100 = 100

I for Tents = 1058.00/800.00 × 100 = 132.35


I for Miscellaneous = 676.00/400.00 = 169.00

Ī= 132.25(15) + 100(0) + 132.25(15) + 100(0) + 100(0) + 132.25(15) +169(30)

15+15+15+30

Ī = 146.95


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.

IMPORTANCE OF INDEX In:

>stock marketS Index numbers are basically economic data information that reflect the price or quantity compared with standard or remnant value. It is normally expressed as 100 times the ratio of the base worth that equals 100. Index numbers are very important for economic analysis. They summarize movements surrounded by a group of related variables. The consumer Price index is one of the most commonly used form of index number. It measures the changes in the retail prices. These index number’s also used to evaluate the condition of the stock market by economic analysis. The up and down of the stock market were identified using index numbers. Therefore index numbers are very important n stock market.


>Property index (PIN)

A PIN (Property Index Number, or also known as a permanent real estate index number) is a numerical code for the legal description of a piece of land as it has been defined for the purposes of real estate taxation. The formatted code points to the parcel's location on the county's tax maps. The best source for your PIN is your deed or tax bill, or other documents you may have from the purchase of your home. If you are not able to locate any of these documents, the Cook County Assessor's website can help you locate a PIN from an address. Therefore index number is very important in property index.


http://www.cookcountyassessor.com/search/

>Environmental awarenessAir 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 colour 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.

We can conclude that the index numbers can even help increase our environmental awareness.


http://en.wikipedia.org/wiki/Ecosystems

http://en.wikipedia.org/wiki/Ozone_depletion

http://en.wikipedia.org/wiki/Stratosphere

http://en.wikipedia.org/wiki/Earth

http://en.wikipedia.org/wiki/Earth's_atmosphere

http://en.wikipedia.org/wiki/Natural_environment

http://en.wikipedia.org/wiki/Biological_material

http://en.wikipedia.org/wiki/Biological_material

http://en.wikipedia.org/wiki/Particulate_matter

http://en.wikipedia.org/wiki/Chemical

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 surroundings like the air and sea, especially in conducting an air-pollution survey. In conclusion, statistics is a daily life necessity. 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.

Also while I was conducting the project, I have learnt and practiced lots of moral values. Some of them are that we should be patient when doing any work or project. This is to ensure our work is completed by time. We also should be calm when any source that we are trying to find comes out fruitless.

Furthermore, we should always be happy so that whatever work we do can be done easily without any tension or panic.


add maths folio form 5

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