JEE Mains · Maths · STD 11 - 13. statistics
If \(\sum \limits_{i=1}^{n}\left(x_{i}-a\right)=n\) and \(\sum \limits_{i=1}^{n}\left(x_{i}-a\right)^{2}=n a,(n, a>1)\) then the standard deviation of \(n\) observations \(x _{1}, x _{2}, \ldots, x _{ n }\) is
- A \(n \sqrt{ a -1}\)
- B \(\sqrt{a-1}\)
- C \(a-1\)
- D \(\sqrt{n(a-1)}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{a-1}\)
Step-by-step Solution
Detailed explanation
\(S.D =\sqrt{\frac{\sum_{i=1}^{n}\left( x _{ i }- a \right)}{ n }-\left(\frac{\sum_{i=1}^{ n }\left( x _{ i }- a \right)}{ n }\right)^{2}}\) \(=\sqrt{\frac{ na }{ n }-\left(\frac{ n }{ n }\right)^{2}}\) \(\left\{\right.\) Given…
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