How to find Pearsonian's Coefficient of Skewness (γ₁)

Question:

Find Pearsonian's Coefficient of Skewness (γ₁) for a distribution when μ₂ = 25 and μ₃ = 100.


Solution:

Step 1: Find β₁

β₁ = μ₃² / μ₂³

β₁ = 100² / 25³

β₁ = (100 x 100) / (25 x 25 x 25)

β₁ = 16 / 25

β₁ = 0.64


Step 2: Find γ₁

γ₁ = ±√β₁

γ₁ = ±√0.64

γ₁ = ± 0.8

∵ μ₃ is positive; γ₁ = + 0.8


Answer:

Pearsonian's Coefficient of Skewness (γ₁) for a distribution is 0.8 when μ₂ = 25 and μ₃ = 100. Since the value of the relative measure of skewness is greater then 0, the distribution is positively skewed.


Video Solution:



How to find Pearsonian's Coefficient of Skewness (γ₁) using solved example from skewness and kurtosis