How do you find the variance and standard deviation of {2,3,4,6,8,9}?

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Answer 1 · 2017-10-12T15:01:54

$sigma^2 = 118/15 ~= 7.867$

$sigma = sqrt(7.8666) = 2.80475786$

Variance of a sample is given by the following equation:

$sigma^2= (sum(x-bar x)^2)/(n-1)$

It can be rearranged to:

$sigma^2 = (Sigmax^2-(Sigmax)^2/n)/(n-1)$

$Sigma(x^2) = 2^2+3^2+4^2+6^2+8^2+9^2 = 210$

$Sigma(x) = 2+3+4+6+8+9 = 32$

$n = 6$

$sigma^2 = (210-(32^2/6))/(6-1) = 118/15 ~= 7.867$

Standard deviation is the square root of variance.

$sigma = sqrt(7.8666) = 2.80475786$