# 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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