Standard deviation is calculated by 1. calculate mean, m 2. calculate deviation of EACH entry of data set from the mean, i.e. d=(x-m) 3. calculate mean of square of deviations (d^2)/n to get variance,v 4. take square-root of variance to get standard deviation.
For example, To find the standard deviation of data set {3,7,8} 1. mean=(3+7+8)/3=6 2. deviations, di={3-6,7-6,8-6}={-3,1,2} 3. squares of deviations, di^2={9,1,4} 4. mean of squares of deviations=(9+1+4)/3=14/3 Standard deviation=sqrt(14/3)=2.16
For the given data set, if you follow the above steps, you would get sum=400 mean=400/9 variance (mean square of deviations)=8246/81 standard deviation=sqrt(8246/81)=sqrt(8246)/9
