JEE Mains · Maths · STD 11 - 13. statistics
A student score the following marks in five tests : \(45, 54, 41, 57, 43\). His score is not known for the sixth test. If the mean score is \(48\) in the six tests, then the standard deviation of the marks in six tests is:
- A \(\frac{10}{3}\)
- B \(\frac{100}{3}\)
- C \(\frac{{100}}{{\sqrt 3 }}\)
- D \(\frac{{10}}{{\sqrt 3 }}\)
Answer & Solution
Correct Answer
(D) \(\frac{{10}}{{\sqrt 3 }}\)
Step-by-step Solution
Detailed explanation
\(AM = \frac{{41 + 45 + 54 + 57 + 43 + x}}{6} = 48\) \( \Rightarrow x = 48\) \({\sigma ^2} + {48^2} = \frac{1}{6}\left( {{{41}^2} + {{45}^2} + {{54}^2} + {{57}^2} + {{43}^2} + {{48}^2}} \right)\) \({\sigma ^2} = \frac{{14024}}{6} - 2304\) \( = \frac{{100}}{3}\)
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