Question 715886
{{{Mean=(6+7+8+9+9+12+15+22)/8=88/8=11}}}


So {{{xbar = 11}}}


Sample Standard Deviation:*[Tex \LARGE   \sigma=\sqrt{ \frac{1}{N-1}\displaystyle\sum_{i=0}^N (x_i-\bar{x})^2}] where *[Tex \LARGE \bar{x}] is the average, *[Tex \LARGE x_i] is the ith number, and *[Tex \LARGE N] is the number of numbers


So we can replace N with 8


*[Tex \LARGE\sqrt{ \frac{1}{8-1}\displaystyle\sum_{i=0}^8 (x_i-\bar{x})^2}]


Subtract {{{8-1}}} to get 7


*[Tex \LARGE\sqrt{ \frac{1}{7}\displaystyle\sum_{i=0}^8 (x_i-\bar{x})^2}]


Replace  *[Tex \LARGE \bar{x}] with 11


*[Tex \LARGE\sqrt{ \frac{1}{7}\displaystyle\sum_{i=0}^8 (x_i-11)^2}]


Expand the summation (replace each {{{x[i]}}} with the respective number)



{{{sqrt((1/7)((6-11)^2+(7-11)^2+(8-11)^2+(9-11)^2+(9-11)^2+(12-11)^2+(15-11)^2+(22-11)^2))}}}


Subtract the terms in the parenthesis


{{{sqrt((1/7)((-5)^2+(-4)^2+(-3)^2+(-2)^2+(-2)^2+(1)^2+(4)^2+(11)^2))}}}


Square each term


{{{sqrt((1/7)(25+16+9+4+4+1+16+121))}}}


Add up all of the terms


{{{sqrt((1/7)196)}}}


Multiply


{{{sqrt(28)}}} 


Take the square root


{{{5.29150262212918}}} This is is the sample standard deviation



The sample variance is simply the square of the sample standard deviation, so the sample variance is 28.