JEE Main 2024 (Online) 9th April Evening ShiftQuestion 1
If the variance of the frequency distribution
$x$ : $c,2c,3c,4c,5c,6c$
$f$ : $2,1,1,1,1,1$
is $160$, then the value of $c\in\mathbb{N}$ is
Statistics
Solution
Value $c$ occurs twice, others once: $N=7$. $\sum fx=c(2+2+3+4+5+6)=22c$, $\sum fx^2=c^2(2+4+9+16+25+36)=92c^2$. Var $=\frac{92c^2}{7}-\frac{484c^2}{49}=\frac{160c^2}{49}=160\Rightarrow c^2=49$, $c=7$. Option B.