INDEX NUMBERS FOR STATISTICS GCE O LEVELS/IGCSE

INTRODUCTION

Index number is a statistical measure of average change in a variable or a group of variables with respect to time or space. The variable may be the cost of commodity or goods. 2 years are compared to see the changes in price. Index number generally computed on annual basis.

Definition:

Index number is a statistical measure that is used to show changes in price, quantify or value of an item or group of related items with respect to time, place or other characteristics.

In order to calculate an index number, a base period needs to be identified. Values in the current period are than compared to the base period.

The index numbers for the base period is 100. The index number for the current period is

then compared to 100.

SIMPLE PRICE INDEX

Index number is called a simple index when it is computed for a single variable. Index number on index number of gold prices, etc

Simple Price Index= P1/P2 x 100

P1=price of item in a given year

P2=price of item in a base year

PRICE RELATIVE

The base year is the particular year with which the prices in other years of that commodity can be compared with. A relative price is the price of a commodity such as a good or service in terms of another; i.e., the ratio of two prices. A relative price may be expressed in terms of a ratio between any two prices or the ratio between the price of one particular good and a weighted average of all other goods available in the market. Source= http://en.wikipedia.org/wiki/Relative_price

SIMPLE AGGREGATE INDEX

It is useful when finding index for group of item. It is one that indicates the percentage changes in the aggregate price of a number of Commodities, at different periods.

Simple aggregate index = ∑p₁/∑p₀ x 100

∑p₁=Total of prices of all commodities in given year

∑p₀ = Total of prices of all commodities in base year

Example

Cost of foods are shown below

	vegetable	Rice	Milk	Total
2010	$50	$20	$10	$80
2011	$55	$25	$8	$88

Using 2010 as a base year, find the simple aggregate index for the total cost for 2011.

Simple aggregate index =∑p₁/∑p₀ x 100

Simple aggregate index =88/80 x 100

Simple aggregate index =110

This shows that price has rise by 10 percent in the 2011 compared to 2010.

WEIGHTED AGGREGATED PRICE INDEX

An index is called a weighted aggregative index when it is constructed for an aggregate of items (prices) that have been weighted in some way so as to reflect their importance.

Weighted aggregate index number = ∑IW/∑W

∑IW= Price of item in given year.

∑W= Price of item in base year.

W= Weights

I=Price Relative

How to calculate Weights

By taking ratios of the

1. Expenditure on different items.

2. Quantities used of different items

Example

	2010	2011	Weights for 2010	Price relative(I)	IW
X	20	35	8	35/20 x 100=175	1400
Y	30	40	4	40/30 x 100=133.33	533.32
Z	60	64	3	64/60 x 100=106.67	320.01
A	90	94	6	94/90 x 100=104.44	626.64
B	20	40	10	40/20 x 100=200	2000
TOTAL			31		4879.97

Weighted aggregate index number = ∑IW/∑W

Weighted aggregate index number =4879.97/31

Weighted aggregate index number =157.42

USES OF INDEX NUMBER

1. The price index numbers are used to measure changes in a particular group of prices and help us in comparing the movement in prices of one commodity with other.
2. A common use of index number is to deflect a future value so that it can be compared with the base period.
3. They are also used to forecast business condition of a country.
4. It is a statistical device used by the government to revise wages, salaries, pensions, social welfare schemes and design future planning.