JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 1
For the frequency distribution : Variate $(x)$: $x_1,x_2,x_3,\ldots,x_{15}$, Frequency $(f)$: $f_1,f_2,f_3,\ldots,f_{15}$ where $0<x_1<x_2<x_3<\ldots<x_{15}=10$ and $\sum_{i=1}^{15}f_i>0$, the standard deviation cannot be :
Statistics
Solution
All values lie in $(0,10]$. The maximum possible variance of data in an interval of length $L$ is $L^2/4$ (attained only at the endpoints). Here, with $x_1>0$, the s.d. is strictly less than $5$. So s.d. $=6$ is impossible; $4,2,1$ are attainable. Option (A).