The mean and variance of n observations x 1 ,   x 2 ,   x 3 , … ,   x n are 5 and 0…

The mean and variance of n observations x1, x2, x3,…, xn are 5 and 0 respectively. If ∑i=1nxi2=400, then the value of n is equal to
  1. 80
  2. 25
  3. 20
  4. 16

Solution

The variance of n observation is σ2=1n∑i=1nxi2-x¯2, where x¯ is the mean of the observations.

Hence, putting the given values, we get

0=1n400-52

⇒400n=25

⇒n=16.

Asked in: AP EAMCET 2021 (19 Aug Shift 2)

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