Business statistics (Basic concepts of Index Numbers)

 Simple and weighted index numbers
 Concept of weights
 Types of index numbers
 Business index number
 CPT, WPI
 Production Index.

 Of the important statistical devices and techniques, Index Numbers have today
become one of the most widely used for judging the pulse of economy, although in
the beginning they were originally constructed to gauge the effect of changes in
prices
 Today we use index numbers for cost of living, industrial production, agricultural
production, imports and exports, etc.
 Index numbers are the indicators which measure percentage changes in a variable
(or a group of variables) over a specified time.

According to Patternson :
" In its simplest form, an index number is the ratio of two index numbers
expressed as a percent . An index is a statistical measure, a measure designed to
show changes in one variable or a group of related variables over time, with respect
to geographical location or other characteristics".
According to Tuttle :
"Index number is a single ratio (or a percentage) which measures the combined
change of several variables between two different times, places or situations".

 An index number, which is designed keeping, specific objective in mind, is a very
powerful tool.
 For example, an index whose purpose is to measure consumer price index, should
not include wholesale rates of items and the index number meant for slumcolonies
should not consider luxury items like A.C., Cars refrigerators, etc

 Price Index :
Measure changes in price over a specified period of time. It is basically the ratio of
the price of a certain number of commodities at the present year as against base
year.
 Quantity Index:
As the name suggest, these indices pertain to measuring changes in volumes of
commodities like goods produced or goods consumed etc.
 Value Index:
These pertain to compare changes in the monetary value of imports ,exports
,production or consumption of commodities.

 Unit Test
 Circular Test
 Time Reversal Test
 Factor Reversal Test

Suppose one is interested in
comparing the sum total
expenditure on a fixed number
of commodities in the year
2003 as against the year 1998 .
Let us consider the following
example.

 Since all the commodities are
in different units and their
prices are not enlarged
proportionally, we just cannot
get an average for comparison.
For that reason, we express
the rates of all commodities in
1998 as 100 each and proportionally increase for the corresponding commodities
for 2003.

 We find that the average number (Index) for 2003 is 156.83 as against 100 for the
year 1998.
 We can say that the prices have gone up by 56.83% in the year 2003 as against
1998.
 This method is used for finding price index numbers.

 Construct the price index number for 2003, , taking the year 2000 as base year

 The price index for the year 2003,taking 2000 as base year is 137.5,showing that
There is an increase of 37.5%in the prices in 2003 as against 2000.

 Consumer Price Index Number (CPI)
 Aggregate Expenditure Method
 Family Budget Method
 Whole Sale Price Index Number (WPI)
 Production Index

Business statistics (Basic concepts of Index Numbers)

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