# Index Number , Data Analysis and Modeling || Bcis Notes

## Index Number

1 Introduction:
Index number measures the relative change in the value of the variable with respect to time. For example, they are used to measure the change in the price of the commodity, income status of the people, the employment rate of the people, price hike, etc with respect to some base period. It is always expressed in percentage form for comparison, the index number for the base period is always equal to 100%.

2 Types:
i) Price Index Number: It measures the change in the price of the commodity at the current period as compared to some base period (reference period) and it is denoted by ‘P’.
ii) Quantitative Index Number: It measures the change in the volume (quantity) of the commodity at the current period as compared to some base period (reference period) and it is denoted by ‘Q’.
iii) Value Index Number: The product of price and quantity of any commodity is called the value of that commodity. It measures the change in the value of the commodity at the current period as compared to some base period (reference period) and it is denoted by ‘V’.

Note:
a. Base period: The period which is selected for comparison is called base period or reference period and it is denoted by suffix ‘0’
b. Current period: The period for which comparison is required is called the current period i.e. the period in which comparison is made is called the current period and it is denoted by suffix ‘i’.

3 Basic notations:
P0 = Price at the base period.
Q0 = Quantity at the base period.
V0 = Value at the base period.

Pi = Price at the current period ( i = 1, 2, 3, 4, ….).
Qi = Quantity at the current period ( i = 1, 2, 3, 4, ….).
Vi = Value at the current period ( i = 1, 2, 3, 4, ….).

P0i = Price index number for the current period ‘i’ with respect to base period ‘0’.
Q0i = Quantity index number for the current period ‘i’ with respect to base period ‘0’.
V0i = Value index number for the current period ‘i’ with respect to base period ‘0’.

Note: Value is the product of price and quantity which is obtained by the following relation.
V0 = P0 X Q0
Vi = Pi X Qi
V0i = P0i X Q0i
W= Weight assigned to the commodities according to their relative importance in the group.

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