In an experiment with 15 observations the results were available and $\sum X^2=2830, \sum X=170$, one…

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
  1. $78.00$
  2. $188.66$
  3. $83.30$
  4. $177.33$

Solution

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

Asked in: MHT CET 2022 (06 Aug Shift 1)

Practice more Statistics questions on Aicharya