JEE Mains · Maths · STD 11 - 13. statistics
If mean and standard deviation of \(5\) observations \(x_1 ,x_2 ,x_3 ,x_4 ,x_5\) are \(10\) and \(3\), respectively, then the variance of \(6\) observations \(x_1 ,x_2 ,.....,x_3\) and \(-50\) is equal to
- A \(509.5\)
- B \(586.5\)
- C \(582.5\)
- D \(507.5\)
Answer & Solution
Correct Answer
(D) \(507.5\)
Step-by-step Solution
Detailed explanation
\(\sum {x = 50} \) \({\left( 3 \right)^2} = \frac{1}{5}\left( {e{x^2} - \frac{{{{\left( {ex} \right)}^2}}}{5}} \right)\) \(9 = \frac{1}{5}\left( {\sum {{x^2} - \frac{{2500}}{5}} } \right)\) \(\therefore \sum {{x^2} = 545} \) New variable…
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