If the observations 1 , 2 , 3 , … . , n occur with frequency n , n - 1 , n - 2 , . . , 1 respectively such that the mean of observations is 13 3 , then n is equal to

Question

If the observations 1 , 2 , 3 , … . , n occur with frequency n , n - 1 , n - 2 , . . , 1 respectively such that the mean of observations is 13 3 , then n is equal to, 10, 11, 12, 13

MARKS App · Accepted Answer

Mean = ∑ f i x i ∑ f i = ∑ r = 1 n r n + 1 - r n n + 1 2 = 13 3 (given) ⇒ n n + 1 2 · n + 1 - n n + 1 2 n + 1 6 n n + 1 2 = 13 3 ⇒ n + 1 - 2 n + 1 3 = 13 3 ⇒ n 3 + 2 3 = 13 3 ⇒ n = 11

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