(i) For a symmetrical distribution
Mean = Mode = Median
(ii) For a moderately asymmetrical distributions
Mode = Median – Mean
Measure of Dsipersion:
(i) Range -:
The range is the difference between two extreme observations
i.e. Range =
Where, = Greatest observation of distribution
= Lowest observation of distribution
(ii) Mean Deviation (M.D) -:
For a set of observations the mean deviation about an average (mean/median/mode) is given by
For a frequency distribution
(iii) Standard Deviation (S.D) -:
Standard deviation is defined as the positive square root of the arithmetic mean of the squares of the deviations of the given values from their arithmetic mean.
For frequency distribution
Standard deviation is regarded as the best measure of dispersion because it satisfies almost all the properties of an ideal measure of dispersion.
(iv) Variance -:
Square of the standard deviation is called as variance .
Root Mean Square Deviation (S):
Mean Square Deviation -:
Analysis of Frequency Distribution -:
The coefficient of variation is defined as
Where and are the standard deviation and mean of the data, respectively.
Shortcut Method to Find Variance -:
Shortcut Method to Find Standard Deviation -: