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.

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