Question 1115412
mean of

{{{5}}}, {{{8}}}, {{{8}}}, {{{9}}}, {{{14}}}, {{{18}}}, {{{100}}} is: 

{{{(5+8+8+9+14+18+100)/7=162/7}}} ≈ {{{23.143}}}


and standard deviation is:

The standard deviation  of a probability distribution is defined as the square root of the variance.

To find the variance, subtract the mean from each of the x values,

{{{5-23.143 = -18.143}}}
{{{8-23.143= -15.143}}}
{{{8-23.143 = -15.143}}}
{{{9-23.143 = -14.143}}}
18-23.143 = -5.143
{{{100-23.143=76.857}}}

Now square all the answers you have got from subtraction.

{{{(-18.143)^2 =329.168449}}}
{{{(-15.143)^2 =229.310449}}}
{{{(-15.143)^2 =229.310449}}}
{{{(-14.143)^2 = 200.024449}}}
{{{(-5.143)^2 = 26.450449}}}
{{{(76.857)^2 = 5906.998449}}}


Add all the Squared numbers,

{{{329.168449 + 229.310449 + 229.310449 + 25 + 200.024449+ 26.450449+5906.998449 = 6946.262694}}}

Divide the sum of squares by {{{(n-1) }}} to get variance

 {{{variance=6946.262694/(n-1)}}} .... and in your case {{{n=7}}}
 {{{variance=6946.262694/6}}}
 {{{variance=1157.710449}}}

Find the square root of variance=standard deviation, 

{{{sqrt(1157.710449)=34.02514436)}}}≈ {{{34.03}}}