Question

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

Answer 1

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`