Question

Calculate combined standard deviation from the following data: 

n₁ = 30, n₂ = 50 x̄ = 23 x̄₂ = 45 ; σ₁= 8, σ₂ = 12

Answer 1

First compute combined mean

The combined standand deviation:

Here d₁² = (x̄₁ – x̄)² = (23-36.75)² = 189.06 

and d₂² = (x̄₂ -x̄)² = (45-36.75)² = 68.06

σ = 15.08