Let x 1 , x 2 , … x n be n observations such that ∑ x i 2 = 500 and ∑ x i = 100 . Then, an impossible value of n among the following is

Question

Let x 1 , x 2 , … x n be n observations such that ∑ x i 2 = 500 and ∑ x i = 100 . Then, an impossible value of n among the following is, 24, 18, 29, 22

MARKS App · Accepted Answer

Variance = ∑ x i 2 n - ∑ x i n 2 ≥ 0 ⇒ ∑ x i 2 n ≥ ∑ x i 2 n 2 ⇒ n ≥ ∑ x i 2 ∑ x i 2 ⇒ n ≥ 10000 500 ⇒ n ≥ 20

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