JEE Mains · Maths · STD 11 - 13. statistics
Let in a series of \(2 n\) observations, half of them are equal to \(a\) and remaining half are equal to \(-a.\) Also by adding a constant \(b\) in each of these observations, the mean and standard deviation of new set become \(5\) and \(20 ,\) respectively. Then the value of \(a^{2}+b^{2}\) is equal to ....... .
- A \(425\)
- B \(650\)
- C \(250\)
- D \(925\)
Answer & Solution
Correct Answer
(A) \(425\)
Step-by-step Solution
Detailed explanation
Let observations are denoted by \(x _{i}\) for \(1 \leq i< 2 n\) \(\bar{x}=\frac{\sum x_{i}}{2 n}=\frac{(a+a+\ldots+a)-(a+a+\ldots+a)}{2 n}\) \(\Rightarrow \overline{ x }=0\) and…
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