Q240 / 270 · NDA 2013 (Phase 2) · Mathematics

The variance of 20 observations is 5 . If each observation is multiplied by 2 , then what is the new variance of the resulting observations?

  • A
    5
  • B
    10
  • Correct answer
    C
    20
  • D
    40

Solution

Variance $\left(\sigma^2\right)=\sum_{i=1}^n f\left(x_i-\overline{\mathrm{X}}\right)^2$ when each observation is multiplied by $m$, then, Variance $\left(\sigma^2\right)=\sum_{i=1}^n m^2 f\left(x_i-\overline{\mathrm{X}}\right)^2$ Here, $m=2$, so, new variance $\left(\sigma^2\right)$ $=2^2 \times 5=20$

Hence, the correct answer is option: 'C'.

Relevant Questions