Question

What is the standard deviation of the data set `78, 90, 456, 676, 111, 381, 21` rounded to the nearest tenth?

Answer 1

Standard Deviation is `229.1`

Explanation:

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

Hence mean is `1/7(78+90+456+676+111+381+21)=1813/7=259`

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

`(Sigmax^2)/N=1/7(78^2+90^2+456^2+676^2+111^2+381^2+21^2)`

= `1/7(6084+8100+207936+456976+12321+145161+441)=837019/7`

Hence Standard Deviation is `sqrt[837019/7-(259)^2`

= `1/7sqrt(837019xx7-259^2xx49)=1/7sqrt(5859133-3286969)=sqrt2572164/7=1603.8/7=229.1`