Question

What is the variance of {-7, 12, 14, 8, -10, 0, 14}?

Answer 1

`2.55 (3s.f.)`

Explanation:

`{-7, 12, 14, 8, -10, 0, 14}`

mean:

`(-7+ 12+ 14+ 8+ -10 + 0+ 14)/7`

`=31/7`

find deviations of each number (`n`-mean):

`-7 - 31/7 =- 49/7 - 31/7 = 80/7`

`12 - 31/7 = 84/7 - 31/7 = 53/7`

`14 - 31/7 = 98/7 - 31/7 = 67/7`

`8 - 31/7 = 56/7 - 31/7 = 25/7`

`-10 - 31/7 = -70/7 - 31/7 = -101/7`

`0 - 31/7 = -31/7`

`14 - 31/7 = 98/7 - 67/7 = 32/7`

variance = mean of deviations:

`(80/7 +53/7+ 67/7+ 25/7 -101/7 -31/7 +32/7)/7`

`=125/49`

`=2.55 (3s.f.)`