Index Number In Our Daily Life

Name : Muhammad Afiq Naim Bin Abdullah

Class : 5 AlfaI/C no : 951208-01-5871

Teacher : En. Alias Bin Md Shah

The objectives of carry out the project work are:

-To apply and adapt variety of problem- solving strategies to solve problems.-To improve thinking skills.-To promote effective mathematical communication.-To develop mathematical knowledge through problem solving in a way that increases students interest and confidence.-To use the language of mathematics to express mathematical ideas precisely.-To provide learning environment that stimulates and enhances effective learning.-To develop positive attitude towards mathematics.

First of all, I would like to say Alhamdulillah to Allah for giving me strength and good health condition to do the project work. Not forgetting my

parents for providing money to buy anything related to this project work. They also supported me and encouraged me to complete the project work.

Other than that, I would to say thank you to our additional mathematics teacher Mr Alias Bin Md Shah for guiding me throughout this project. He

helps me a lot especially when I facing a problem in this project work. Finally , thank you to my friends who shared their ideas with me to

complete the project work successfully.

Title Page

Foreword

Content

Introduction

Part 1

Part 2

Further Exploration

Index numbers are meant to study the change in the effects of such factors which cannot be measured directly. According to Bowley, ³Index numbers are used to measure the changes in some quantity which we cannot observe directly´. For example, changes in business activity

in a country are not capable of direct measurement but it is possible to study relative changes in business activity by studying the variations in the values of some such factors

which affect business activity, and which are capable of direct measurement. Index numbers are commonly used statistical device for measuring the combined fluctuations in a group related variables. If we wish to compare the price level of consumer items today with that

prevalent ten years ago, we are not interested in comparing the prices of only one item, but in comparing some sort of average price levels. We may wish to compare the present

agricultural production or industrial production with that at the time of independence. Here again, we have to consider all items of production and each item may have undergone a

different fractional increase (or even a decrease). How do we obtain a composite measure. This composite measure is provided by index numbers which may be defined as advice for

combining the variations that have come in group of related variables over a period of time, with a view to obtain a figure that represents the ‘net’ result of the change in the constitute

variables.

Index numbers may be classified in terms of the variables that they are intended to measure.

In business, different groups of variables in the measurement of which index number techniques are commonly used are (i)price, (ii) quantity, (iii) value and (iv) business activity.

Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value of exports and index of business activity, etc. Here we shall be mainly

interested in index numbers of prices showing changes with respect to time , although methods described can be applied to other cases. In general, the

present level of prices is compared with the level of prices in the past. The present period is

called the current period and some period in the past is called the base period.Index Numbers:

Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc. A collection of index numbers for different years, locations, etc., is

sometimes called an index series.Simple Index Number :

A simple index number is a number that measures a relative change in a single variable with respect to a base.

Composite Index Number : A composite index number is a number that measures an average relative changes in a

group of relative variables with respect to a base.

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 different categories. 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.(b) Record the items and their prices systematically in a table. Since items maybe differently packed, be sure to use consistent measurements for each item selected so that comparison can be done easily and accurately.(c) Create a suitable graphical representations to compare and contrast the price of the items chosen.(d) Based on the graphical in (c ) , Interpret and discuss your findings.(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.

(a)

Item Price(RM)

Shop A Shop B Shop C

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

B.

(c )

(D)

Based on the graphical representations that I have construct in 1(c), there is small difference in the price of sugar only but the price difference between Self-Raising Flour, Butter, Eggs. The graph 1(D) will show the conclusion of the difference among the shops based upon the shops total price.

(E)The item that has a large price difference among the shops is Eggs.

The price difference of the Eggs is due to the standard of the shop and the type of company that supply the Eggs although the Eggs have same grade. The expensive Eggs maybe have been cleaned through a certain processes

and the higher price means a higher quality.

Every year SMK Tun Abdul Razak organizes a carnival to raise funds for the school. Last year , during the carnival , Your class made and sold a cakes. Because of the popularity of the cakes , Your class has decided to carry out the same project for this year’s carnival.(A) Suggest a shop from part 1 which you would go to purchase the ingredients for the cakes. State and discuss your reasons for purchasing from the shop you suggested.(B) Construct a table which four main ingredients that you use with the quantity , price in year before and price this year.(C ) Calculate the price index for each of the ingredients in table in (B) for the year 2012 based on the year 2011.(D) Calculate the composite index for making a cake in the year 2012 based on the year 2011. Discuss your findings.(E) in the year 2011, the cakes was sold at RM 12.00 each. Suggest a suitable selling price for the cakes in the year 2012. Give reasons for your answer.

(A)The shop that I would go to purchase the Ingredients is Shop C because the total price of shop C is the lowest between the other shop.(B)

(C )

Ingredients Quantity Price in the year 2011(RM)

Price in the year 2012(RM)

Self-Raising Flour 250 g 0.85 0.90

Sugar 200 g 0.30 0.36

Butter 250 g 4.20 4.30

Eggs 5 Eggs(300g) 0.40 0.42

Ingredients Quantity Price in the year 2011(RM)

Price in the year 2012(RM)

Price index for the year 2012 based on the year 2011(I)

Self-Raising Flour

250 g 0.85 0.90 105.88

Sugar 200g 0.30 0.36 120

Butter 250 g 4.20 4.30 102.38

Eggs 5 Eggs(300g)

0.40 0.42 105

(D)

The composite index of the ingredients used for making a cake is 105.32 . The increasing in the index number of the ingredients is mainly due to the increasing price of the petroleum every year.

Ingredients Weightage (W)

Self-Raising Flour

250/1000 = 1/4

Sugar 200/1000 = 1/5

Butter 250/250 = 1

Eggs 300/720= 5/12

(E)

The most suitable price of the cake in the year 2012 is RM 12.64 . The cake was sold at the price of RM 12.00 in the year 2011. The price of the cake need to be increased due to the rise of the ingredients.

Further ExplorationIndex 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 calculateair 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 byan anticyclone or temperature inversion, or other lack of winds lets air pollution remain in a local area . Indices by locationSouth KoreaThe Ministry of Environment of South Korea uses the Comprehensive 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 value sof the five air pollutants, the highest is the CAI value.

The concept may be extended well beyond an exchange. The Dow ones 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&P500 index:price return, which only considers the price of the components, total return, which accounts for dividen investment, and net total return, which accounts for dividen investment 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 to 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 acountry’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 index number 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 important. 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.