What are the variance and standard deviation of {1, 1, 1, 1, 1, 7000, 1, 1, 1, 1, 1, 1, 1, 1, 1}?

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Answer 1 · 2016-12-17T21:44:23

$variance = 3,050,000(3s.f.)$
$Sigma = 1750 (3s.f.)$

first find the average:

average = $(1+1+1+1+1+7000+1+1+1+1+1+1+1+1+1)/15$

$= 7014/15$

$= 467.6$

find deviations for each number- this is done by subtracting the average:

$1 - 467.6 = -466.6$

$7000 - 467.6 = 6532.4$

then square each deviation:

$(-466.6)^2 = 217,715.56$

$6532.4^2 = 42,672,249.76$

the variance is the mean of these values:

variance = $((14 * 217715.56) + 42672249.76) / 15$

$= 3,050,000(3s.f.)$

the standard deviation is the square root of the variance:

$Sigma = sqrt(3050000) = 1750 (3s.f.)$