Let x1, x2,...........,xn be n observations such that [ x_i^2 = 400] and [ x_i = 80].

Question

Let x1, x2,...........,xn be n observations such that

$$\sum {x_i^2}  = 400$$ and $$\sum {{x_i}}  = 80$$. Then a
possible value of n among the following is

Accepted Answer

As we know,

$${\sigma ^2} \ge 0$$

$$\therefore\,\,\,$$ $${{\sum {x_i^2} } \over n} - {\left( {{{\sum {{x_i}} } \over n}} \right)^2} \ge 0$$

$$ \Rightarrow \,\,\,{{400} \over n} - {{6400} \over {{n^2}}} \ge 0$$

$$ \Rightarrow \,\,\,n \ge 16$$

$$\therefore\,\,\,$$ Possible value of n according to the option is = 18

Solutions · 1