\(\text { Average Deviation }=\frac{1}{n}\sum_{i=1}^{n}|x-\bar{x}|\)

**x**represents the observation.

\(\bar{x}\) represents the mean.

**n**represents the number of observations.

### Solved Examples

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

**Solution:**

First lets find the mean by using the formula,

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

$\overline{x} = 9$

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

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

$Average \: Deviation=3$

**Question 2: **Find the average deviation for the following set of observations.

11, 6, 6, 12, 12, 7, 7, 9

**Solution:**

Given set of observations:

11, 6, 6, 12, 12, 7, 7, 9

Sum of observations = 11 + 6 + 6 + 12 + 12 + 7 + 7 + 9 = 70

Number of observations = n = 8

Mean = Sum of observations/Total number of observations

\(\bar{x}=\frac{70}{8}=8.75\\ Average\ deviation = \frac{\left | 11-8.75 \right | +\left | 6-8.75 \right |+ \left | 6-8.75 \right |+\left | 12-8.75 \right |+\left | 12-8.75 \right |+\left | 7-8.75 \right |+\left | 7-8.75 \right |+\left | 9-8.75 \right |}{8}\)

\(=\frac{2.25+ 2.75+ 2.75+ 3.25+ 3.25+ 1.75+1.75+ 0.25}{8}\\=\frac{18}{8}\\=2.25\)