Given data points are #28, 30, 29, 26, 31# and #30#, find standard deviation step by step?

1 Answer
Oct 25, 2017

Standard Deviation is #1.633#

Explanation:

Arithmetic Mean is simply sum of all data points divided by their number and as here data points are #28, 30, 29, 26, 31# and #30#, their mean is

#(28+30+29+26+31+30)/6=174/6=29#

Deviations from mean are values of data points minus arithmetc mean and here they are #28-29=-1#, #30-29=1#, #29-2=0#, #26-29=-3#, #31-29=2# and #30-29=1# respectively.

Squares of the deviations are #1,1,0,9,4# and #1#.

As variance is average of square of the deviations , variance is #(1+1+0+9+4+1)/6=16/6=8/3=2.6667#

and Standard Deviation is square root of variance i.e. #sqrt2.6667=1.633#