Average Deviation Formula

The average deviation formula is used to characterize the dispersion among the given set of data. The average deviation is the average deviation of each observation from the mean value of the observation. The mean of the observations is calculated before the average deviation is calculated. The average deviation formula becomes a handy tool to quickly calculate the average deviation and reach the result very quickly. Let us study the average deviation formula using solved examples.

What Is Average Deviation Formula?

The average deviation formula is used to calculate the average deviation of the observation from the mean value of the observation. The average deviation formula for n number of observations is given below:

Average Deviation = 1/nΣ|\(x_i\) - x̅|

where

• \(x_i\)= Data values in the given set.
• x̅ is the mean.
• n is the total number of data values

Let's take a quick look at a couple of examples to understand the average deviation formula, better.

Examples on Average Deviation Formula

Example 1: Find the average deviation of the given data using the average deviation formula: 12, 14, 16, 18, 20, 22.

Solution:

To find: average deviation 
Given: n = 6
Finding mean of the given data:
x̅ = (12 +14 + 16 + 18 + 20 + 22)/6 = 17
Using the  average deviation formula
Average deviation = (|12 - 17| + |14 - 17| + |16 - 17| + |18 - 17| + |20 - 17| + |22 - 17|)/6
= (5 + 3 + 1 + 1 + 3 + 5)/6 = 18/6 = 3
Average deviation = 3

Answer: Hence the average deviation of the given data is 3.

Example 2: Find the average deviation of the given data using the average deviation formula: 33, 44, 55, 66, 77, 88, 99.

Solution:

To find: average deviation 
Given: n = 7
Goinding mean of the given data:
x̅ = (33 + 44 + 55 + 66 + 77 + 88 + 99)/7 = 66
Using the  average deviation formula,
Average deviation = (|33 - 66| + |44 - 66| + |55 - 66| + |66 - 66| + |77 - 66| + |88 - 66| + |99 - 66|)/7
Average deviation = 18.857

Answer: Hence the average deviation of the given data is 18.857.

Example 3: A football player played 5 games so far this season. The scoring numbers from each game are 14, 10, 9, 7, and 5. Determine the mean and calculate the average deviation.

Solution:The average of the score is = (14 + 10 + 9 + 7 + 5)/5 = 45/5 = 9
the average score = 9
To calculate the average deviation we need to calculate the deviation from the average for each game.
|14 - 9| = 5
|10 - 9| = 1
|9 - 9| = 0
|7 - 9| = 2 
|5 - 9| = 4
Sum of variations = 5 + 1 + 0 + 2 + 4 = 12
Average deviation = 12/5 = 2.4

Answer: Hence the average deviation of the given data is 2.4