Understanding Skewness: Analyzing Data Asymmetry

Skewness means ‘Lack of Symmetry’. Skewness give an idea about the shape of the curve which can draw with the help of the given data. A distribution is said to be skewed if -

1. Mean, Median & Mode fall at different points, i.e., Mean ≠ Median ≠ Mode.
2. Quartiles are not equidistant from median.
3. The curve drawn with the help of the given data is not symmetrical but stretched to one side than other side.

Measures of Skewness

1. Sk = M - Md
2. Sk = M - Mo
3. Sk = (Q3 - Md) - (Md - Q1) where M is mean, Md is median, Mo is mode, Q1 is first quartile and Q3 is third quartile.

Prof Karl Pearson’s Coefficient of skewness

Sk = (M - Mo)/ σ If mode is ill-defined, then use empirical relation Mo = 3Md - 2M Sk = 3(M - Md)/σ

Limit of Karl Pearson coefficient of skewness: -3≤Sk≤3

Prof Bowley’s Coefficient of skewness

Sk = Q3 -Q1 - 2Md/ Q3 - Q1

Limit of Bowley coefficient of skewness: -1≤Sk≤1