JEE Main 2022 (Online) 30th July Evening ShiftQuestion 1
If the mean and median of the data $x$: $0$-$10$, $10$-$20$, $20$-$30$, $30$-$40$, $40$-$50$ with frequencies $f$: $3,6,2,x,y$ and $\sum f=20$ are equal, then $xy^2$ is equal to
Statistics
Solution
$3+6+2+x+y=20\Rightarrow x+y=9$. Mean $=\frac{15+90+50+35x+45y}{20}=\frac{155+35x+45y}{20}$. Cumulative frequencies $3,9,11$: median class is $20$-$30$, median $=20+\frac{10-9}{2}\cdot10=25$. Mean $=25\Rightarrow35x+45y=345\Rightarrow7x+9y=69$, with $x+y=9$: $2y=6$, $y=3,x=6$ (cum $11\ge10$ OK). $xy^2=6\cdot9=54$. Option A.