JEE Main 2026 (Online) 5th April Evening ShiftQuestion 1
A variable $X$ takes values $0,0,2,6,12,20,\ldots,n(n-1)$ with frequencies ${}^{n}C_0,{}^{n}C_1,{}^{n}C_2,{}^{n}C_3,{}^{n}C_4,{}^{n}C_5,\ldots,{}^{n}C_n$ respectively. If the mean of this data is $60$, then its median is :
Statistics
Solution
Mean $=\frac{\sum {}^nC_k\,k(k-1)}{2^n}=\frac{n(n-1)2^{n-2}}{2^n}=\frac{n(n-1)}{4}=60\Rightarrow n(n-1)=240\Rightarrow n=16$. Values $k(k-1)$ increase with $k$ and frequencies ${}^{16}C_k$ are symmetric about $k=8$, so the median is the value at $k=8$. Median $=8\cdot7=56$. Option A.