Skewness and Kurtosis

It refers to asymmetry of any distribution. The symmetry of a distribution means that from a given deviation from a central value, there are equal number of observations on either side of the it.

If the distribution is asymmetrical or skewed, its frequency curve would have a prolonged tail either towards its left or right hand side.

Hence the Skewness of a distribution is defined as the departure form symmetry.

Symmetric or Normal Distribution

For a symmetrical distribution

Mean = Median = Mode

Positively Skewed

For Positively Skewed distribution

Mode < Median < Mean

(i.e. more values are on the right hand side of the distribution than left)

Negatively Skewed

For Negatively Skewed distribution

Mean < Median < Mode

(i.e. more values are on the left hand side of the distribution than Right)

Measures of Skewness

1. Based on Measure of Mean, Median and Mode.

2. Based on Quartiles and Percentiles.

3. Based on Moments.

Based on Measure of Mean, Median and Mode

Based on Quartiles and Percentiles

Known as Bowly’s Coefficient of Skewness

Value of coefficient of Skewness lies between - 1 and + 1

Based on Moments

Measures of Kurtosis

A measure of coefficient of Kurtosis is given by Karl Pearson; That says if