Measures of Variability

Measures of variability or spread

Measures of variability, also known as measures of spread, show us the dispersion in the dataset and how the data is distributed around the center (measure of location) of the dataset. The most commonly used measures of variability are discussed below:

Variance

The variance is the expected value (mean) of the squared differences of the data values from the mean. It shows us how close or far the values in a dataset are from the mean of the dataset in squared units.

Formula

$s^2={\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2}$

• $s^2$ is the variance.

• $n$ is the total number of values in the dataset

• $\sum_{i=1}^n$ is the sum of the values from 1 to n.

• $(x_i-\bar{x})^2$ is the square of the difference of each value in the dataset from the mean.

• $\sum_{i=1}^n(x_i-\bar{x})^2$ is the sum of all the squared differences of values from the mean.

Example

• Let’s say we have a list of numbers as 34, 56, 190, 10000, and 45.

• Here $n$ = 5 (number of values)

• The mean of the above list of numbers is calculated as:

$\bar{x}=\frac{34 + 56 + 190 + 10000 + 45}{5}=\frac{10325}{5}=2065$

• The calculations are done below:

x	x-x̄	(x-x̄)$^2$
34	-2031	4124961
56	-2009	4036081
190	-1875	3515625
10000

...