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
- A \(78.00\)
- B \(188.66\)
- C \(83.30\)
- D \(177.33\)
Answer & Solution
Correct Answer
(A) \(78.00\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { correct } \Sigma x^2=2830-20^2+30^2=3330 \\ & \text { correct } \Sigma x=170-20+30=180 \\ & \text { correct variance }=\frac{1}{15} \Sigma x^2-\left(\frac{1}{15} \Sigma x\right)^2 \\ & =\frac{1}{15} \times 3330-\left(\frac{1}{15} \times 180\right)^2 \\ & =222-144 \\ & =78\end{aligned}\)
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