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

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Answer 1 · 2016-12-29T14:08:10

$2.55 (3s.f.)$

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

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:

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

$=125/49$

$=2.55 (3s.f.)$