JEE Mains · Maths · STD 11 - 13. statistics
The mean and standard deviation of \(20\) observations are found to be \(10\) and \(2\), respectively. On respectively, it was found that an observation by mistake was taken \(8\) instead of \(12\) . The correct standard deviation is
- A \(\sqrt{3.86}\)
- B \( 1.8\)
- C \(\sqrt{3.96}\)
- D \(1.94\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3.96}\)
Step-by-step Solution
Detailed explanation
Mean \((\bar{x})=10\) \( \Rightarrow \frac{\Sigma \mathrm{x}_{\mathrm{i}}}{20}=10 \) \( \Sigma \mathrm{x}_{\mathrm{i}}=10 \times 20=200\) If \(8\) is replaced by \(12\) , then \(\Sigma x_1=200-8+12=204\) \(\therefore\) Correct mean…
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