JEE Mains · Maths · STD 11 - 13. statistics
The mean and standard deviation of \(15\) observations are found to be \(8\) and \(3\) respectively. On rechecking it was found that, in the observations, \(20\) was misread as \(5\) . Then, the correct variance is equal to......
- A \(7\)
- B \(20\)
- C \(19\)
- D \(17\)
Answer & Solution
Correct Answer
(D) \(17\)
Step-by-step Solution
Detailed explanation
We have \(\text { Variance }=\frac{\sum\limits_{ r =1}^{15} x _{ r }^{2}}{15}-\left(\frac{\sum\limits_{ r =1}^{15} x _{ r }}{15}\right)^{2}\) Now, as per information given in equation \(\frac{\sum x _{ r }^{2}}{15}-8^{2}=3^{2} \Rightarrow \sum x _{ T }^{2}=\log 5\) Now, the new…
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