Statistics – Skewness:

A fundamental task in any statistical analyses is to characterize the location and variability of a data set. A distribution of data item values can be symmetrical or asymmetrical. Skewness is asymmetry in a statistical distribution, where the curve appears distorted or skewed either to the left or to the right. Skewness can be quantified to what extent a distribution differs from a normal distribution.

In a normal distribution, the graph appears as a symmetrical “bell-shaped curve(the tails on either side of the curve are exact mirror images of each other).” At the maximum point on the curve the mean, median, mode are equal(in Normal distribution). Therefore are all said to be appropriate measure of central tendency.

When a histogram is constructed for skewed data it is easy to identify skewness by the shape of the distribution.

A distribution is positively skewed when the tail on the right side of the histogram is longer than the left side. Most of the values tend to cluster toward the left side of the x-axis with increasingly fewer values at the right side of the x-axis

A distribution is said to be negatively skewed when the tail on the left side is longer than the right side of the histogram.

According to Karl Pearson, coefficient of skewness can be calculated as

Mode skewness coefficient(first skewness coefficient) =  

Median skewness coefficient(second skewness coefficient) =

To calculate “Skewness” (the amount of skew), we use the SKEW() function in Excel.