Skewness

(i) Meaning, types and Objectives of Skewness

Meaning. Skewness means asymmetricity of the distribution of a statistical series.It is opposite to the symetrical nature of a series. In a symmetric series, the following characteristics are found:

Characteristic of a Symmetric Series

• The values of the series when plotted on a graph paper give a bell shaped curve as under:

 

 

 

 

 

• The values of Mean, Median and Mode are identical.
• Both the extreme quartiles i.e. Q₃ are equidistant from the Median i.e. (Q₃ – M) = (M – Q1).
• Both the extreme Percentiles, and Deciles are equidistant from the Median.

i.e.          (P₉₀ – M) = (M – P₁₀), and

                (D₉ – M ) = (M – D₁)

• The sum of the positive diviations from Median is equal to the sum of the negative deviations from Median i.e. ∑(X-M) =0
• The frequencies are equally distributed at the points of equal deviations from Mode.
• B₁ (Beta one) is equal to zero.
• B₂ (Beta two) is equal to 3.
• Y₁ (Gamma one) is equal to zero.