How to find μ₂ for a distribution

Question:

Find μ₂ for a distribution when the distribution is mesokurtic and μ₄ = 108?

Step 1: Note the given data.

The distribution is mesokurtic, hence γ₂ = 0.

μ₄ = 108

Step 2: Find β₂

γ₂ = β₂ - 3

∴ 0 = β₂ - 3

∴ β₂ = 3

Step 3: Find μ₂

β₂ = μ₄ / μ₂²

∴ 3 = 1024 / μ₂²

∴ μ₂² = 1024 / 3

∴ μ₂² = 36

∴ μ₂ = √36

∴ μ₂ = 6

μ₂ for a distribution is 6 when the distribution is mesokurtic and μ₄ = 108.