Q76 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is

  • A
    $37$
  • B
    $42$
  • C
    $247$
  • Correct answer
    D
    $252$

Solution

$n=50$ $\begin{aligned} & \sigma^2(x)=7 \\ & \because \sigma^2(a x+b)=a^2 \cdot \sigma^2(x) \\ & \sigma^2(6 x-5)=6^2 \cdot \sigma^2(x)=36 \times 7=252\end{aligned}$

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

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