JEE Main 2023 (Online) 1st February Evening ShiftQuestion 1
Let $9=x_1<x_2<\ldots<x_7$ be in an A.P. with common difference $d$. If the standard deviation of $x_1,x_2,\ldots,x_7$ is $4$ and the mean is $\overline x$, then $\overline x+x_6$ is equal to :
Statistics
Solution
Variance of 7 terms of an A.P. $=\frac{d^2(49-1)}{12}=4d^2=16$, so $d=2$. Terms $9,11,\ldots,21$: $\bar x=15$, $x_6=19$, sum $=34$.