Skewness is the degree of asymmetry, or departure from symmetry, of a distribution.
For skewness distribution, the mean tends to lie on the same side of the mode as the longer tail.
In many books measure of skewness is denoted by , J or Sk.
Different formulae for measuring skewness are:
i) Bowley's formula for measuring skewness in terms of quartiles is:
ii) Kelley gave the formula in terms of percentiles and deciles. Kelley's absolute measures os skewnes are:
These formulae are not practically used. Instead, it is measured as coefficient of skewness which is given as:
Kelly's formulae are seldom used.
iii) Karl Pearson's measure of skewness:
iv) Karl pearson's formulae for a wide class of frequency distributions in terms of moments is
gives only the measure of skewness but not the direction of skewness. So another measure is defined as:
How to interpret the value of measure of skewness:
Calculate the coefficient of skewness of the following data by using Karl Pearson's method.
2 3 3 4 4 6 6
Step 1. Find the mean:
Step 2. Find the standard deviation:
Step 3. Find the coefficient of skeness: (negative skewness)