JEE Advanced 2026 Paper 2Question 1
Consider a data consisting of 10 observations $x_1,x_2,\ldots,x_{10}$, whose mean is $5$ and variance is $7$. If the mean and the variance of the first $8$ observations $x_1,x_2,\ldots,x_8$ are $4$ and $3.5$, respectively, and $x_9<x_{10}$, then the value of $3x_9+2x_{10}$ is ____________.
Statistics
Answer$44$
Solution
$x_9+x_{10}=50-32=18$; $\sum x^2=10(7+25)=320$, first eight $8(3.5+16)=156$, so $x_9^2+x_{10}^2=164$. Then $x_9x_{10}=80$, giving $8,10$ with $x_9<x_{10}$. $3(8)+2(10)=44$.