What is the variance of {-3, -6, 7, 0, 3, -2}?

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Answer 1 · 2018-06-17T16:14:33

$211/2 or 105.5$

find the mean:

$-3 + -6 + 7 + 0 + 3 + 2 = 3$

$3/6 = 1/2$

subtract the mean from each number in the data and square the result:

$-3 - 1/2 = -7/2$
$-6 - 1/2 = -13/2$
$7 - 1/2 = 13/2$
$0 - 1/2 = -1/2$
$3 - 1/2 = 5/2$
$2 - 1/2 = 3/2$

$(-7/2)^2 = 49/4$
$(-13/2)^2 = 169/4$
$(13/2)^2 = 169/4$
$(-1/2)^2 = 1/4$
$(5/2)^2 = 25/4$
$(3/2)^2 = 9/4$

find the mean of the squared differences:

$49/4 + 169/4 + 169/4 + 1/4 + 25/4 + 9/4 = 422/4 = 211/2 or 105.5$