What is the variance of 2, 9, 3, 2, 7, 7, 12?

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Answer 1 · 2017-01-28T03:11:17

$14.bar6$

The formula for the variance of a data set is

$s^2=1/(n-1)sum_(k=1)^n(x-barx)_k^2$

in this case $n=7$

and

$barx=1/nsum_(k=1)^n x_k=(2+9+3+2+7+7+12)/7=(11+5+14+12)/7=(16+26)/7=42/7=6$

Then

$s^2=1/6sum_(k=1)^7(x-6)_k^2=((-4)^2+3^2+(-3)^2+(-4)^2+1^2+1^2+6^2)/6=(16+9+9+16+2+36)/6=(32+18+2+36)/6=88/6=44/3=14.bar6$