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#