Question 734489
The sample mean is the average and is computed as the sum of all the observed outcomes  from the sample divided by the total number of events.


{{{mean=(11+17+24+ 26+27+29+34+42)/8}}}


{{{mean=210/8}}}


{{{mean=26.25}}}


 Variance and Standard Deviation: Step by Step

    Calculate the mean,{{{ x}}}.


{{{x=26.25}}}

    Write a table that subtracts the mean from each observed value.

{{{x }}}-------	{{{x - 26.25}}}------- 	{{{(x - 26.25 )^2 }}} 

{{{11}}}-------{{{ -15.25}}}-------     	{{{232.5625}}}

{{{17}}} -------            {{{ -9.25}}}-------      	{{{85.5625}}}

{{{24}}}-------             {{{ -2.25}}}-------      	{{{5.0625}}}

{{{26}}}-------             {{{ -0.25}}}-------      	{{{0.0625}}}

{{{27}}}-------             {{{ 0.75}}}-------      	{{{0.5625}}}

{{{29}}}-------             {{{ 2.75}}}-------      	{{{7.5625}}}

{{{34}}}-------             {{{ 7.75}}}-------      	{{{60.0625}}}

{{{42}}}-------             {{{ 15.75}}}-------      	{{{248.0625}}}



Total: {{{232.5625+85.5625+5.0625+0.0625+0.5625+7.5625+60.0625+248.0625            =639.5}}}

    
    Divide {{{639.5}}} by {{{n -1}}} where {{{n=8}}} is the number of items in the sample.

{{{639.5/8=79.9375}}}  This is the {{{variance}}}.

    To get the {{{standard}}} {{{deviation}}} we take the square root of the variance.  

  {{{sqrt(79.9375)=8.94}}}