Question

`If x_1, x_2, .....x_n` are n observations such that `sum_(i=1)^n (x_i)^2=400` and `sum_(i=1)^n x_i=100` then possible values of n among the following is (1) 18 (2) 20 (3) 24 (4) 27

Answer 1

AM of `m^(th)` power>`m^(th)`power of AM
`((x_1^m+x_2^m...+x_n^m)/n)>((x_1+x_2+x_3+..+x_n)/n)^m`
Lets take m=2
`(x_1^2+x_2^2+...+x_n^2)/n>(x_1+x_2+x_3+...+x_n)/n^2`
`sumx_i^2/n>[sumx_i]^2/n^x`
`n>100^2/400`
`n>25`
option 4 is correct.