Question 1133608


Standard Deviation,

{{{22}}} ,{{{29}}} ,{{{21}}}, {{{24}}} ,{{{27}}}, {{{28}}}, {{{25}}} ,{{{36}}}

First, work out the average, or arithmetic mean, of the numbers:

{{{mu=(22+29+21+24+27+28+25 +36)/8=26.5}}}

{{{N =8}}}

Then, take each number, subtract the mean and square the result:

{{{22-26.5=-4.5}}}
{{{29-26.5=2.5}}}
{{{21-26.5=-5.5}}}
{{{24-26.5=-2.5}}}
{{{27-26.5=0.5}}}
{{{28-26.5=1.5}}}
{{{25 -26.5=-1.5}}}
{{{36-26.5= 9.5}}}

Square of each difference:

{{{(-4.5)^2}}}, {{{2.5^2}}},{{{ (-5.5)^2}}}, {{{(-2.5)^2}}},{{{ 0.5^2}}}, {{{1.5^2}}},{{{ (-1.5)^2}}}, {{{9.5^2}}}={{{20.25}}}, {{{6.25}}}, {{{30.25}}},{{{ 6.25}}}, {{{0.25}}}, {{{2.25}}}, {{{2.25}}}, {{{90.25}}}

Now calculate the Variance:

add up the squared differences and divide by count

{{{(20.25+6.25+30.25+ 6.25+ 0.25+ 2.25+ 2.25+90.25)/8=158/8=19.75}}}

Lastly, take the square root of the Variance: 


{{{sqrt(19.75)=4.444097209}}}->the sample standard deviation