# Average Deviation Formula

The average deviation is a part of several indices of variability that is used by statisticians to characterize the dispersion among the measures in a given population. The average deviation of a set of scores is calculated by computing the mean and then specific distance between each score and that mean without regard to whether the score is above or below the mean. It is also called as average absolute deviation. Below mentioned is the formula to calculate the average deviation.

$\LARGE Average\:Deviation=\sum_{i=1}^{n}\left | x-\overline{x} \right |$

Where,
x, represents the observation.
$bar{x}$, represents the mean.
n, represents the number of observation.

### Solved Examples

Question 1: Calculate the average deviation for the given data: 4, 6, 8, 10, 12, 14?
Solution:

Given:
n = 6
First lets find the mean by using the formula,

$\overline{x} = \frac{4+6+8+10+12+14}{6}$

$\overline{x} = 9$

$Average \: Deviation= \frac{\left | 9-4 \right |\left | 9-6 \right |\left | 9-8 \right |\left | 10-9 \right |\left | 12-9 \right |\left | 14-9 \right |}{6}$

$Average \: Deviation=\frac{5\times 3\times 1\times 1\times 3\times 5}{6}$

$Average \: Deviation=37.5$