JEE Mains · Maths · STD 11 - 13. statistics
Let the mean and variance of \(12\) observations be \(\frac{9}{2}\) and \(4\) respectively. Later on, it was observed that two observations were considered as \(9\) and \(10\) instead of \(7\) and \(14\) respectively. If the correct variance is \(\frac{m}{n}\), where \(m\) and \(n\) are co-prime, then \(m + n\) is equal to
- A \(316\)
- B \(314\)
- C \(317\)
- D \(315\)
Answer & Solution
Correct Answer
(C) \(317\)
Step-by-step Solution
Detailed explanation
\(\frac{\sum x }{12}=\frac{9}{2}\) \(\sum x =54\) \(\frac{\Sigma x ^2}{12}-\left(\frac{9}{2}\right)^2=4\) \(\sum x ^2=291\) \(\sum x _{\text {new }}=54-(9+10)+7+14=56\) \(\sum x _{\text {new }}^2=291-(81+100)+49+196=355\)…
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