Question

What is the standard deviation of the data set `87, 21, 90, 43, 54, 23, 123, 110, 90, 44,` and `50`?

Answer 1

Standard Deviation is `33.11`

Explanation:

The mean of data set is given by the sum of data divided by their number i.e. `(Sigmax)/N`

Hence mean is `1/11(87+21+90+43+54+23+123+110+90+44+50)=735/11`

Standard Deviation is given by `sqrt[(Sigmax^2)/N-((Sigmax)/N)^2`

`(Sigmax^2)/N=1/11(87^2+21^2+90^2+43^2+54^2+23^2+123^2+110^2+90^2+44^2+50^2)`

= `1/11(7569+441+8100+1849+2916+529+15129+12100+8100+1936+2500)=61169/11`

Hence Standard Deviation is `sqrt[61169/11-(735/11)^2`

= `1/11sqrt(61169xx11-735^2)=1/11sqrt(672859-540225)=sqrt132634/11=364.1895/11=33.11`