According to Professor Bowley, averages are “statistical constants which enable us to comprehend in a single effort the significance of the whole.” They give us an idea about the concentration of the values in the central part of the distribution. Plainly speaking, an average of a statistical series is the value of the variable which is representative of the centric distribution. The following are three measures of central tendency that are in common use:
i) Arithmetic Mean or simply Mean,
ii) Median, and
Requisites for an Ideal Measure of Central Tendency
It should be rigidly defined.
It should be readily comprehensible and easy to calculate.
It should be based on all the observations.
It should be suitable for further mathematical treatment.
It should be affected as little as possible by fluctuations of sampling.
It should not be affected much by extreme values.Arithmetic Mean: Arithmetic mean of a set of observations is their sum divided by the number of observations. If x1, x2, x3,………, xn are n observations, the arithmetic mean of this series x is,
x = ——- (x1 + x2 + x3 +………, + xn)
Arithmetic mean from raw data
Arithmetic mean from grouped data
Arithmetic mean of a number of means (Weighted mean)
Median: Median of a distribution is the value of the variable which divides it into two equal parts. It is a positional average.
Median of a distribution with even number of observations
Median of a distribution with odd number of observations
Mode: Mode is the value which occurs most frequently in a set of observations and around which the other items of the set cluster densely. A distribution can have more than one mode. If there are two modes we can say it as bi-modal distribution.