JEE Mains · Maths · STD 11 - 13. statistics
If the variance of \(10\) natural numbers \(1,1,1, \ldots ., 1, k\) is less than \(10 ,\) then the maximum possible value of \(k\) is ...... .
- A \(12\)
- B \(11\)
- C \(14\)
- D \(21\)
Answer & Solution
Correct Answer
(B) \(11\)
Step-by-step Solution
Detailed explanation
\(\sigma^{2}=\frac{\Sigma x ^{2}}{ n }-\left(\frac{\Sigma x }{ n }\right)^{2}\) \(=\frac{9+ k ^{2}}{10}-\left(\frac{9+ k }{10}\right)^{2}<10\) \(90+10 k^{2}-81-k^{2}-18 k < 1000\) \(9 k ^{2}-18 k -991 < 0\) \(k^{2}-2 k < \frac{991}{9}\) \(( k -1)^{2} < \frac{1000}{9}\)…
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