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Quantitative Techniques – I

Notes While taking weighted average of price relatives, the values are often taken as weights.
These weights can be the values of base year quantities valued at base year prices.
In case of weighted aggregative price index numbers, quantities are often taken as weights.
These quantities can be the quantities purchased in base year or in current year or an
average of base year and current year quantities or any other quantities.

A quantity index number measures the change in quantities in current year as compared
with a base year.
Index numbers where comparisons of various periods were done with reference to a
particular period, termed as base period. Such type of index number series is known as
fixed base series.

10.12 Keywords

Barometers of economic activity: Sometimes index numbers are termed as barometers of
economic activity.

Base Year: The year from which comparisons are made is called the base year. It is commonly
denoted by writing ‘0’ as a subscript of the variable.
Current Year: The year under consideration for which the comparisons are to be computed is
called the current year. It is commonly denoted by writing ‘1’ as a subscript of the variable.
Dorbish and Bowley’s Index: This index number is constructed by taking the arithmetic mean of
the Laspeyres’s and Paasche’s indices.

Fisher’s Index: Fisher suggested that an ideal index should be the geometric mean of Laspeyres’
and Paasche’s indices.
Index number: An index number is a statistical measure used to compare the average level of
magnitude of a group of distinct but related variables in two or more situations.
Kelly’s Fixed Weights Aggregative Index: The weights, in this index number, are quantities
which may not necessarily relate to base or current year. The weights, once decided, remain
fixed

Laspeyres’s Index: Laspeyres’ price index number uses base year quantities as weights
Marshall and Edgeworth’s Index: This index number uses arithmetic mean of base and current
year quantities.

Paasche’s Index: This index number uses current year quantities as weights.
Quantity Index Number: A quantity index number measures the change in quantities in current
year as compared with a base year.

Simple Aggregative Method: In this method, the simple arithmetic mean of the prices of all the
items of the group for the current as well as for the base year are computed separately. The ratio
of current year average to base year average multiplied by 100 gives the required index number

Value index Number: A value index number gives the change in value in current period as
compared with base period. The value index is denoted by V01. for all periods
Walsh’s Index: Geometric mean of base and current year quantities are used as weights in this
index number.
Weighted Aggregative Method: This index number is defined as the ratio of the weighted arithmetic
means of current to base year prices multiplied by 100.

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