Page 143 - DMGT404 RESEARCH_METHODOLOGY

Unit 8: Descriptive Statistics

8.2 Various Measures of Average Notes

Various measures of average can be classified into the following three categories:
1. Mathematical Averages:
(a) Arithmetic Mean or Mean
(b) Geometric Mean
(c) Harmonic Mean

(d) Quadratic Mean
2. Positional Averages:
(a) Median
(b) Mode
3. Commercial Average:
(a) Moving Average
(b) Progressive Average
(c) Composite Average
The above measures of central tendency will be discussed in the order to their popularity. Out of
these, the Arithmetic Mean, Median and Mode, being most popular, are discussed in that order.

8.2.1 Arithmetic Mean

Before the discussion of arithmetic mean, we shall introduce certain notations. It will be assumed
that there are n observations whose values are denoted by X , X , ..... X , respectively. The sum of
1 2 n
these observations X + X + ..... + X will be denoted in abbreviated form as,
1 2 n
n
 i X
i 1
where S (called sigma) denotes summation sign. The subscript of X, i.e., ‘i’ is a positive integer,
which indicates the serial number of the observation. Since there are n observations, variation
in i will be from 1 to n. This is indicated by writing it below and above S, as written earlier. When
there is no ambiguity in range of summation, this indication can be skipped and we may simply
write X + X +..... + X = SX .
1 2 n i
Arithmetic Mean is defined as the sum of observations divided by the number of observations.
It can be computed in two ways:
1. Simple arithmetic mean and

2. Weighted arithmetic mean
In case of simple arithmetic mean, equal importance is given to all the observations while in
weighted arithmetic mean, the importance given to various observations is not same.

Calculation of simple arithmetic mean can be done in following ways:
1. When Individual Observations are Given
Let there be n observations X , X ..... X . Their arithmetic mean can be calculated either by
1 2 n
direct method or by short cut method. The arithmetic mean of these observations will be
denoted by X .
(a) Direct Method: Under this method, X is obtained by dividing sum of observations by
number of observations, i.e.,

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