JEE Mains · Maths · STD 11 - 13. statistics
The mean and standard deviation of \(20\) observations were calculated as \(10\) and \(2.5\) respectively. It was found that by mistake one data value was taken as \(25\) instead of \(35 .\) If \(\alpha\) and \(\sqrt{\beta}\) are the mean and standard deviation respectively for correct data, then \((\alpha, \beta)\) is :
- A \((11,26)\)
- B \((10.5,25)\)
- C \((11,25)\)
- D \((10.5,26)\)
Answer & Solution
Correct Answer
(D) \((10.5,26)\)
Step-by-step Solution
Detailed explanation
Given : Mean \((\bar{x})=\frac{\Sigma x_{i}}{20}=10\) or \(\Sigma \mathrm{x}_{\mathrm{i}}=200\) (incorrect) or \(200-25+35=210=\Sigma \mathrm{x}_{\mathrm{i}}\) (Correct) Now correct \(\bar{x}=\frac{210}{20}=10.5\) again given \(S . D=2.5(\sigma)\)…
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