JEE Mains · Maths · STD 11 - 13. statistics
The mean and standard deviation of \(10\) observations are \(20\) and \(84\) respectively. Later on, it was observed that one observation was recorded as \(50\) instead of \(40\). Then the correct variance is:
- A \(14\)
- B \(13\)
- C \(12\)
- D \(11\)
Answer & Solution
Correct Answer
(B) \(13\)
Step-by-step Solution
Detailed explanation
\(\mu=20, \sigma=8\) \(\mu_{\text {Corrected }}=\frac{200-50+40}{10}=19\) \(\sigma^2=\frac{1}{10} \sum x_i^2-20^2\) \((64+400) 10=\sum x_i^2\) \(\sigma_{\text {Corrected }}^2=\frac{1}{10}[(64+400) 10-2500+1600]-19^2\) \(=374-361\) \(=13\)
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