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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