JEE MAIN - Mathematics (2005 - No. 8)
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
$$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a possible value of n among the following is
18
15
12
9
توضیح
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
$${\sigma ^2} \ge 0$$
$$\therefore\,\,\,$$ $${{\sum {x_i^2} } \over n} - {\left( {{{\sum {{x_i}} } \over n}} \right)^2} \ge 0$$
$$ \Rightarrow \,\,\,{{400} \over n} - {{6400} \over {{n^2}}} \ge 0$$
$$ \Rightarrow \,\,\,n \ge 16$$
$$\therefore\,\,\,$$ Possible value of n according to the option is = 18