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13.Statistics
medium
સંખ્યાઓ $8,21,34,47, \ldots, 320$, નું વિચરણ મેળવો.
A$1059$
B$1238$
C$7562$
D$8788$
(JEE MAIN-2025)
Solution
$8+( n -1) 13=320$
$13 n =325$
$n =25$
$\text { no. of terms }=25$
$\text { mean }=\frac{\sum x _{ i }}{ n }=\frac{8+21+\ldots+320}{25}=\frac{\frac{25}{2}(8+320)}{25}$
$\text { variance } \sigma^2=\frac{\sum x _{ i }^2}{ n }-(\text { mean })^2$
$=\frac{8^2+21^2+\ldots .+320^2}{13}-(164)^2$
$=8788$
$13 n =325$
$n =25$
$\text { no. of terms }=25$
$\text { mean }=\frac{\sum x _{ i }}{ n }=\frac{8+21+\ldots+320}{25}=\frac{\frac{25}{2}(8+320)}{25}$
$\text { variance } \sigma^2=\frac{\sum x _{ i }^2}{ n }-(\text { mean })^2$
$=\frac{8^2+21^2+\ldots .+320^2}{13}-(164)^2$
$=8788$
Standard 11
Mathematics
