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# Average Deviation Formula

Average deviation, also called as "average absolute deviation" helps us to know the value that deviates from its average value among the given group of data.

The Average deviation is calculated in three simple steps:
1. Determine the mean by adding all the numbers and dividing by the number of observation.
2. Now find the deviation of each value by subtracting it with the mean value.
3. In order to get the average deviation, add the deviation of all the values and divide it by the number of observation.
The formula is given by:

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

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## Average Deviation Problems

Below are the problems based on Average absolute deviation :

### Solved Examples

Question 1: Calculate the average deviation for the given data: 2, 4, 6, 8, 10 ?
Solution:

Given:
n = 5
First lets find the mean by using the formula,
$\bar{x}$ = $\frac{\sum x}{n}$

$\bar{x}$ = $\frac{2+4+6+8+10}{5}$

$\bar{x}$ = $\frac{30}{5}$

$\therefore$ Mean = 6
Now, lets calculate the deviation of each value
For $x_{i}$ = 2, $\left |x _{i}-\bar{x}\right |$ = $\left | 2 - 6 \right |$ = 4
For $x_{i}$ = 4, $\left |x _{i}-\bar{x}\right |$ = $\left | 4 - 6 \right |$ = 2
For $x_{i}$ = 6, $\left |x _{i}-\bar{x}\right |$ = $\left | 6 - 6 \right |$ = 0
For $x_{i}$ = 8, $\left |x _{i}-\bar{x}\right |$ = $\left | 8 - 6 \right |$ = 2
For $x_{i}$ = 10, $\left |x _{i}-\bar{x}\right |$ = $\left | 10 - 6 \right |$ = 4

Average deviation = $\frac{\sum_{i=1}^{n}x-\bar{x} }{n}$

= $\frac{12}{5}$

= 2.4

Question 2: Find average deviation for following data: 52, 54, 56, 58 60 ?
Solution:

Given:
n = 5
First lets find the mean by using the formula,

$\bar{x}$ = $\frac{\sum x}{n}$

$\bar{x}$ = $\frac{52+54+56+58+60}{5}$

$\bar{x}$ = $\frac{280}{5}$

$\therefore$ Mean = 56

Now, lets calculate the deviation of each value
For $x_{i}$ = 52, $\left |x _{i}-\bar{x}\right |$ = $\left | 52 - 56 \right |$ = 4
For $x_{i}$ = 54, $\left |x _{i}-\bar{x}\right |$ = $\left | 54 - 56 \right |$ = 2
For $x_{i}$ = 56, $\left |x _{i}-\bar{x}\right |$ = $\left | 56 - 56 \right |$ = 0
For $x_{i}$ = 58, $\left |x _{i}-\bar{x}\right |$ = $\left | 58 - 56 \right |$ = 2
For $x_{i}$ = 60, $\left |x _{i}-\bar{x}\right |$ = $\left | 60 - 56 \right |$ = 4

Average deviation = $\frac{\sum_{i=1}^{n}x-\bar{x} }{n}$

= $\frac{12}{5}$

= 2.4

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