# Skewness

Lack of symmetry is called skewness. If a distribution is not symmetrical then it is called a skewed distribution. So, the mean, median and mode are different in value and one tail becomes longer than the other. The skewness may be positive or negative.

__Positively Skewed Distribution__

If the frequency curve has a longer tail to right, the distribution is known as a positively skewed distribution and ** Mean > Median > Mode**.

__Negatively Skewed Distribution__

If the frequency curve has a longer tail to left, the distribution is known as a negatively skewed distribution and ** Mean < Median < Mode**.

__Measure of Skewness__

The difference between the mean and mode gives an absolute measure of skewness. If we divide this difference by the standard deviation we obtain a relative measure of skewness known as the coefficient and denoted by * SK*.

Karl Pearson Coefficient of Skewness

\[SK = \frac{{Mean – Mode}}{{S.D}}\]

Sometimes the mode is difficult to find. So we use another formula:

\[SK = \frac{{3\left( {Mean – Median} \right)}}{{S.D}}\]

Bowley’s Coefficient of Skewness

\[SK = \frac{{{Q_1} + {Q_3} – 2Median}}{{{Q_3} – {Q_1}}}\]