Question

What is the variance of the following numbers?: 63, 54, 62, 59, 52,

Answer 1

`sigma^2 = 18.8`

Explanation:

`mean = (63 + 54 + 62 + 59 + 52)/5`
`mean = 58`
`n = 5`

63
`x - mean = 63 - 58 = 5`
`(x - mean)^2 = 5^2 = 25`

54
`x - mean = 54 - 58 = -4`
`(x - mean)^2 = (-4)^2 = 16`

62
`x - mean = 62 - 58 = 4`
`(x - mean)^2 = 4^2 = 16`

59
`x - mean = 59 - 58 = 1`
`(x - mean)^2 = 1^2 = 1`

52
`x - mean = 52 - 58 = -6`
`(x - mean)^2 = (-6)^2 = 36`

`Sigma(x - mean)^2 = 25 + 16 + 16 + 1 + 36 = 94`

`sigma^2 = (Sigma(x - mean)^2)/n = 94/5 = 18.8`