Question

The mean and variance of n observations x₁ ,x₂, x₃, ..., x_n are 5 and 0, respectively. If `sum_(x = 1)^n x_i^2` = 400, then the value of n is equal to ______.

Options

• 80

• 25

• 20

• 16

Answer 1

The mean and variance of n observations x₁ ,x₂, x₃, ..., x_n are 5 and 0, respectively. If `sum_(x = 1)^n x_i^2` = 400, then the value of n is equal to 16.

Explanation:

`overlinex` = 5, variance = `1/n sumx_i^2 - (x)^2`

`\implies` 0 = `1/n . 400 - 25`

`\implies` n = `400/25` = 16