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Mean Absolute Deviation Formula

Average absolute deviation of the collected data set is the average of absolute deviations from a center point of the data set. Abbreviated as MAD, Mean absolute Deviation has four types of deviations that is derived by central tendency, mean median and mode and standard deviation. Mean absolute deviation is however best used as it is more accurate and easy to use in real life situations.

The formula for Mean Absolute Deviation (MAD) is as follows:

\[\large MAD=\sum_{i-1}^{n}\frac{\left|x_{i}-\overline{x}\right|}{n}\]

Where
xi = input data,
$\bar{x}$ = Mean value for a given set of data,
n = number of data

To find it you need to follow below steps:

  • Calculate the mean for the given set of data.
  • Find the difference between each value present in the data set and the mean that gives you the absolute value.
  • Find the average of all the absolute values got out of the difference between the data set and the mean that gives the mean absolute deviation (MAD).

Solved Examples

Question 1: Find the mean absolute deviation of the following data set 26+46+56+45+19+22+24

Solution:

Given set of data in ascending order can be arranged as 26+46+56+45+19+22+24

Now construct the following table for MAD:

$x_{i}$ $x_{i}-\overline{x}$ $\left|x_{i}-\overline{x} \right|$
26 -8 8
 46 12 12
56 22 22
45 11 11
19 -15 15
22 -12 12
24 -14 -14

Now, Let’s find out the average distance of all the absolute values:

$\frac{(8+12+22+11+15+12+14)}{7}=13.42$

Now, coming to the MAD formula:

$MAD=\sum_{i-1}^{n}\frac{\left|x_{i}-\overline{x}\right|}{n}$

$MAD=\frac{13.42}{7}=1.91$

 

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