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SKEWNESS

Skewness is a measure of symmetry of the shape of frequency distribution, i.e., it reveals the dispersal of value on either side of an average is symmetrical or not.

There are four mathematical measures of relative skewness. 

(a) Karl Pearson's Coefficient of Skewness

lf mode is ill-defined, then we take

(b) Bowley's Coefficient of Skewness

This is based on quartiles and median and is defined as

This formula is useful when the mode is ill-defined or the distribution has open end classes or unequal class-intervals.

(c) Coefficient of skewness based on central moments Using second and third central moments, the coefficient of skewness is defined as (due to Karl Pearson)

Note. 1. If SK is positive then the frequency distribution is called positively skewed.

If SK is negative then the frequency distribution is called negatively skewed.

If SK is zero, then the frequency distribution is symmetric.

2. There is no theoretical limit to this measure.