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

Question

Lily Thornton · Accepted Answer

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

\frac{28 + 30 + 29 + 26 + 31 + 30}{6} = \frac{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

\frac{1 + 1 + 0 + 9 + 4 + 1}{6} = \frac{16}{6} = \frac{8}{3} = 2.6667

and Standard Deviation is square root of variance i.e.

\sqrt{2.6667} = 1.633

KickAntitte06 · Accepted Answer

Solution
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,

∴ \overset{―}{x} = \frac{28 + 30 + 29 + 26 + 31 + 30}{6} = \frac{174}{6} = 29

Deviations from mean are values of data points minus arithmetic 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 given by,

V a r (X) = \frac{1 + 1 + 0 + 9 + 4 + 1}{6} = \frac{16}{6} = 2.6667

Standard Deviation is square root of variance.

∴ σ_{x} = \sqrt{V a r (X)}

∴ σ_{x} = \sqrt{2.6667}

∴ σ_{x} = 1.633

Given data points are 28,30,29,26,31 and 30, find standard deviation

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