Question 1152846
The mean of numbers {{{3}}},{{{6}}},{{{4}}},{{{x}}} and {{{7 }}}is {{{15}}}.

find the standard deviation

first find {{{x}}}


{{{(3+6+4+x+7 )/5 =15}}}

{{{20+x =15*5}}}

{{{x =75-20}}}

{{{x =55}}}

the standard deviation:

{{{3}}},{{{6}}},{{{4}}},{{{55}}},{{{7 }}}

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

{{{(3-15)^2=144}}}
{{{(6-15)^2=81}}}
{{{(4-15)^2=121}}}
{{{(55-15)^2=1600}}}
{{{(7-15)^2=64}}}
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sum of Differences^2------={{{144+81+121+1600+64=2010}}}

find Variance: Sum of Differences^2 / (Count−1)

{{{Variance=2010/4=502.5}}}

Standard Deviation: the square root of the variance 

{{{delta=sqrt(502.5)}}}≈{{{22.4165}}}