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MHT CET · Maths · Statistics

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. A \(78.00\)
  2. B \(188.66\)
  3. C \(83.30\)
  4. D \(177.33\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(78.00\)

Step-by-step Solution

Detailed explanation

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