This question was previously asked in

SSC CGL Tier-II ( JSO ) 2018 Official Paper ( Held On : 14 Sept 2019 )

Option 1 : 3

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10 Questions
10 Marks
7 Mins

**Given**

Two series of data are given

N_{1 } = 10 and N_{2} = 5

X̅_{1} = 7 and X̅_{2} = 4

σ_{1} = 1 and σ_{2} = 1

Combined mean = X̅ = 6

x̅_{1} and x̅_{2} are mean of two series

**Formula**

Variance of (X_{1} + X_{2}) = [N_{1}(σ^{2}_{1} + D^{2}_{1}) + N_{2}(σ^{2}_{1} + D^{2}_{2})]/(N_{1} + N_{2})

D_{1} = X̅_{1} – X̅

D_{2} = X̅_{2} – X̅

**Calculation**

⇒ D_{1} = 7 – 6 = 1

⇒ D_{2} = 4 – 6 = -2

⇒ Var(X_{1} + X_{2}) = [10(1^{2} + 1^{2}) + 5(1^{2} + (-2)^{2}]/(10 + 5)

⇒ (20 + 25)/15

⇒ 45/15

**∴**** The combined variance is 3**

__Important Points__

Variance is square of standard deviation = σ^{2}

Coefficient of variation = (σ/x̅) × 100