Question

The following information is available for two sections of a factory. Obtain the combined standard deviation of the production time.

	Section A	Section B
No. of workers	10	40
Mean production time per unit (minute)	25	20
Variance	16	25

Answer 1

Section A:

n₁ = No. of workers =10

x̄₁ = Average production time per unit = 25

s₁¹ = Variance =16

Section B :

n₂ = No. of workers = 40

x̄₂ = Average production time per unit = 20

s₂² = Variance = 25

Combine mean of production time per unit of Section A and Section B:

Combined standard deviation of production time per unit of Section A and Section B :

d₁ = x̄₁ – x̄_c = 25 – 21 = 4

∴ d₁² = 16

d₂ = x̄₂ – x̄_c = 20 – 21 = -1

∴d₂¹ = 1

s₁ = 4 ∴ s₁² = 16: s₂ = 5 ∴ s₂² = 25