JEE Main 2025 — Statistics Question with Solution
JEE Main 2025 (23 Jan Shift 2)
Question
The variance of the numbers is
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Show full solutionCorrect answer: 8788
Correct answer
8788
Step-by-step explanation
$\begin{aligned}
& 8+(n-1) 13=320 \\
& 13 n=325 \\
& n=25 \\
& \text { no. of terms }=25
\end{aligned}$
$\begin{aligned}
& \text { mean }=\frac{\sum \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}=\frac{8+21+\ldots+320}{25}=\frac{\frac{25}{2}(8+320)}{25} \\
& \text { variance } \sigma^2=\frac{\sum \mathrm{x}_{\mathrm{i}}^2}{\mathrm{n}}-(\text { mean })^2 \\
& =\frac{8^2+21^2+\ldots .+320^2}{13}-(164)^2 \\
& =8788
\end{aligned}$
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