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Additional Mathematics Project Work 4/2010

STATISTICS IN OUR DAILY LIFEPROJECT 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

CONTENTNO1 2 3 4 5 6 7

CONTENTSIntroduction Appreciation Part 1 Part 2 Part 3 Further Exploration Reflection

Additional Mathematics Project Work 4/2010

IntroductionWe 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 nonExperience classroom environments which are challenging, interesting and Experience classroom environments where knowledge and skills are applied in Experience classroom environments where expressing ones mathematical thinking, Experience classroom environments that stimulates and enhances effective learning. Acquire effective mathematical communication through oral and writing, and to use Enhance acquisition of mathematical knowledge and skills through problem-solving 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 Train ourselves not only to be independent learners but also to collaborate, to Use technology especially the ICT appropriately and effectively Train ourselves to appreciate the intrinsic values of mathematics and to become Realize the importance and the beauty of mathematics routine problems; meaningful and hence improve their thinking skills. meaningful ways in solving real-life problems. reasoning and communication are highly encouraged and expected

the language of mathematics to express mathematical ideas correctly and precisely in ways that increase interest and confidence

problems and hence develop positive attitude towards mathematics. cooperate, and to share knowledge in an engaging and healthy environment

more creative and innovative

Additional Mathematics Project Work 4/2010 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.

AppreciationAlhamdullilah, 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 statisticBy 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 "computerintensive" 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 1The 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

llllllllllllllllllllllllllllllllllllll l

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 1. Self-Raising Flour(1000g) 2. Sugar(1000g) 3. Butter(250g) 4. Eggs (Grade A) 1 dozen Total Price 1. Soap (3 bars) 2.Liquid Mini Market 4.00 2.00 4.70 5.90 16.60 3.20 4.29 18.90 5.50 31.89 1.50 5.00 1.30 1.30 9.10 57.59 PRICE (RM) Pasaraya Segar Discount Store 3.70 3.60 1.90 1.80 4.50 4.30 5.50 5.00 15.60 14.70 3.00 2.80 3.90 3.20 17.00 5.50 29.40 1.30 4.80 1.20 1.20 8.50 53.50 16.50 5.50 28.00 1.00 4.50 1.00 1.10 7.60 50.30

FOOD

dishwasher(1000ml) 3. Clothes detergent (3kg) 4. Toilet Cleaner (500ml) Total Price 1. Sharpener 2. Pencil (2b-1dozen) STATIONERY 3. Pen 4. Eraser Total Price Grand Total

DETERGENT

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

7 6 5 4 3 2 1 0 Mini Market Pasaraya Discount Segar Ctore Self-Raising Flour Sugar Butter Eggs(Grade A)

Additional Mathematics Project Work 4/2010

2)

20 18 16 14 12 10 8 6 4 2 0 Mini Market Pasaraya Discount Segar Store soap(3bar) Liquid dish washer Clothes detergent Toilet cleaner

Additional Mathematics Project Work 4/2010

3)

6 5 Sharpener 4 3 2 1 0 Mini Market Pasaraya Segar Discount Store Pencil2B (1dozen) Pen Eraser

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