Statistics - Skewness

What is a Symmetric data ?

A data set where the left and right hand sides of the distribution are roughly equal .In a histogram ,the tails of the left as well as the right part of the distribution are equally balanced.data Such kinds of data are often referred as symmetric data.

In below case if we calculate the Mean and Median both are approximately equal to 5.5

Mean =5.5

Median =5.5

If we see the tail on the left of the center value is almost equal to the value on the right side of the center.Skewness refers to the asymmetry of lack of symmetry in the frequency distribution.

However, a distribution which is asymmetrical is skewed .skewed can be both positive and negative.

Negative Skewness :- When a distribution is skewed to the left (red dashed curve), the tail on the curve's left-hand side is longer than the tail on the right-hand side, and the mean is less than the mode. This situation is also called negative skewness.

                                    Mean < Mode

Positive Skewness :- When a distribution is skewed to the right the tail on the curve's right-hand side is longer than the tail on the left-hand side, and the mean is greater than the mode. This situation is also called positive skewness.

                                    Mean > Mode

Tests of Skewness :-

1. The values of mean, median and mode do not coincide.

2. When the data are plotted on a graph they do not give the normal bell-

shaped form i.e. when cut along a vertical line through the centre the two

halves are not equal.

3.The sum of the positive deviations from the median is not equal to the sum

of the negative deviations.

4. Quartiles are not equidistant from the median.

5. Frequencies are not equally distributed at points of equal deviation from

the mode

Karl Pearson’s Measure :-

The formula for measuring skewness as given by Karl Pearson is as follows:

                     Skewness = Mean - Mode

Coefficient of Skewness = Mean – Mode / SD