The mean and variance of n observations x 1 , x 2 , x 3 , … , x n are 5 and 0 respectively. If ∑ i = 1 n x i 2 = 400 , then the value of n is equal to

Question

The mean and variance of n observations x 1 , x 2 , x 3 , … , x n are 5 and 0 respectively. If ∑ i = 1 n x i 2 = 400 , then the value of n is equal to, 80, 25, 20, 16

MARKS App · Accepted Answer

The variance of n observation is σ 2 = 1 n ∑ i = 1 n x i 2 - x ¯ 2 , where x ¯ is the mean of the observations. Hence, putting the given values, we get 0 = 1 n 400 - 5 2 ⇒ 400 n = 25 ⇒ n = 16 .

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