How to find μ₃ for a distribution?

Question:

Find μ₃ for a distribution when Pearsonian's Coefficient of Skewness (γ₁) = 1 and Standard Deviation = 4.


Solution:

Step 1: Find μ₂

∵ Standard Deviation = 4, Variance = 4² = 16

Variance = μ₂ = 16


Step 2: Find β₁

γ₁ = √β₁

1 = √β₁

β₁ = 1²

β₁ = 1


Step 2: Find μ

β₁ = μ₃² / μ₂³

1 = μ₃² / 16³

μ₃² = 16 x 16 x 16

μ₃ = √[16 x 16 x 16]

μ₃ = 4 x 4 x 4

μ₃ = 64


Answer:

μ₃ for a distribution is 64 when Pearsonian's Coefficient of Skewness (γ₁) = 1 and Standard Deviation = 4.


Video Solution:



How to find u₃ for a distribution a solved example of skewness and kurtosis