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The variance of given observation is 5. If each observation is multiplied by 2 then find new variance.
1. 20
2. 5
3. 10
4. None of these

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Correct Answer - Option 1 : 20

Concept:

Variance: Let xi for i = 1, 2, 3, …, n be observations then variance is given as:

\(\rm \sigma^2 = \frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n}\)

Properties of variance:

  • Var(X + C) = Var(X), where C is a constant.
  • Var(CX) = C2 × Var(X), where C is a constant.

 

Calculation:

Given: Var(X) = 5

Each observation is multiplied by 2.

So, new variance = Var(2X)

= 22 × 5

= 20

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