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.)#