Question

One set containing 5 numbers has mean =8and variance =24 and the second set contains 3 number has mean=8 and variance=24. The variance of combined set is?

Answer 1

Answer:

24

Step-by-step explanation:

One set containing 5 numbers has mean =8and variance =24 and the second set contains 3 number has mean=8 and variance=24. The variance of combined set is?

n₁ = 5  ,   X₁ = 8  , σ₁ = 24

n₂ = 3  ,   X₂ = 8  , σ₂ = 24

Combined Mean = Xc

Xc  = (n₁ X₁ + n₂X₂)/(n₁ + n₂)  = (5 * 8  + 3*8)/(5 + 3)  = 8

Combined Variance = σc

σc = ( n₁(σ₁ + (X₁-Xc)²) + n₂(σ₂ + (X₂-Xc)²) ) /(n₁ + n₂)

=> σc = ( 5 ( 24 + (8-8)² + 3(24 + (8-8)²) )/(5 + 3)

=> σc = (5 * 24 + 3 * 24)/8

=> σc = (8 * 24)/8

=> σc = 24

The variance of combined set is 24