Refresher - Variance and Standard Deviation

Definition:
The variance is the average of the squares of the distance each value is from the mean. The symbol for the population variance is ${\displaystyle {\sigma }^2}$ ( ${\displaystyle \sigma }$ is the Greek lowercase letter sigma).

The formula for the variance is ${\displaystyle {\sigma }^2=\frac{\Sigma x^2-\left(\frac{{(\Sigma x)}^2}{n}\right)}{n-1}}$ or ${\displaystyle s^2=\frac{\Sigma x^2-\left(\frac{{(\Sigma x)}^2}{n}\right)}{n-1}}$

Where

x = individual value      n= sample size

The standard deviation is the square root of the variance. The population standard deviation is denoted by ${\displaystyle \sigma }$

${\displaystyle \sigma =\sqrt{{\sigma }^2}}$

Note:

• ${\displaystyle \Sigma x^2\ne {(\Sigma x^2)}^2}$
• ${\displaystyle \mu }$: Population Mean    ${\displaystyle {\sigma }^2}$: Population Variance   ${\displaystyle \sigma }$: Population Standard Deviation
  ${\displaystyle \overline{x}}$: Sample Mean            ${\displaystyle s^2}$: Sample Variance           ${\displaystyle s}$: Sample Standard Deviation

Note:

• , If s = 0, all measurements are the same
• The larger the value of , the more variable the data