JEE Mains · Maths · STD 11 - 13. statistics
A data consists of \(n\) observations \({x_1},{x_2},......,{x_n}.\) If \(\sum\limits_{i - 1}^n {{{({x_i} + 1)}^2}} = 9n\) and \(\sum\limits_{i - 1}^n {{{({x_i} - 1)}^2}} = 5n,\) then the standard deviation of this data is
- A \(5\)
- B \(\sqrt 5\)
- C \(\sqrt 7\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(\sqrt 5\)
Step-by-step Solution
Detailed explanation
\({\sum {\left( {{x_i} + 1} \right)} ^2} = 9n\,\,\,\,\,\,....\left( 1 \right)\) \({\sum {\left( {{x_i} - 1} \right)} ^2} = 5n\,\,\,\,\,\,....\left( 2 \right)\) \(\left( 1 \right) + \left( 2 \right) \Rightarrow \sum {\left( {x_i^2 + 1} \right)} = 7n\)…
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