JEE Mains · Maths · STD 11 - 13. statistics
Let the Mean and Variance of five observations \(x_1=1, x_2=3, x_3=a, x_4=7\) and \(x_5=b, a \gt b\), be 5 and 10 respectively. Then the Variance of the observations \(n+x_n, n=1,2, \ldots \ldots . .5\) is
- A \(17\)
- B \(16.4\)
- C \(17.4\)
- D \(16\)
Answer & Solution
Correct Answer
(D) \(16\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \bar{x}=\frac{\sum x_i}{n}=\frac{1+3+a+7+b}{5}=5 \\ & a+b=14 \\ & \sigma^2=\frac{\sum x_i^2}{n}-(\bar{x})^2 \\ & \Rightarrow \frac{1^2+3^2+a^2+7^2+b^2}{5}-25=10 \\ & a^2+b^2=116 \\ & a \gt b \quad a=10 \quad b=4 \\ & n+x_n: 2,5,13,11,9\end{aligned}\)…
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