Let $x_1$, $x_2$, ….. , $x_n$, be n observations such that $\sum{x_i}^2$ = 400 and $\sum{x_i}$ = 80. Then, a possible value of among the following is

Question :

Let $x_1$, $x_2$, ….. , $x_n$, be n observations such that $\sum{x_i}^2$ = 400 and $\sum{x_i}$ = 80. Then, a possible value of among the following is

(a) 12

(b) 9

(c) 18

(d) 15

Solution :

Given  $\sum{x_i}^2$ = 400 and $\sum{x_i}$ = 80

$\because$ $\sigma^2$ $\ge$ 0

$\therefore$  $\sum{x_i}^2\over n$ – $({\sum{x_i}\over n})^2$ $\ge$ 0

$\implies$ $400\over n$ – $6400\over n^2$ $\ge$ 0

$\therefore$   n $\ge$ 16

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