Q93 / 150 · MHT CET 2022 (06 Aug Shift 1) · Mathematics

In an experiment with 15 observations the results were available and $\sum X^2=2830, \sum X=170$, one observation that was 20 , was found wrong and was replaced by the correct value 30 , then the corrected variance is

  • Correct answer
    A
    $78.00$
  • B
    $188.66$
  • C
    $83.30$
  • D
    $177.33$

Solution

$\begin{aligned} & \text { correct } \Sigma x^2=2830-20^2+30^2=3330 \\ & \text { correct } \Sigma x=170-20+30=180 \\ & \text { correct variance }=\frac{1}{15} \Sigma x^2-\left(\frac{1}{15} \Sigma x\right)^2 \\ & =\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2 \\ & =222-144 \\ & =78\end{aligned}$

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

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