Mean Absolute Deviation Formula

Average absolute deviation of the collected data set is the average of absolute deviations from a centre point of the data set. Abbreviated as MAD, Mean absolute deviation has four types of deviations that are 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 values
$\bar{x}$ = Mean value for a given set of data,
n = Number of data values

To find MAD, 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 of the difference between the data set and the mean that gives the mean absolute deviation (MAD).

Solved Example

Question: Find the mean absolute deviation of the following data set:

26, 46, 56, 45, 19, 22, 24.

Solution:

Given set of data is:

26, 46, 56, 45, 19, 22, 24

Mean = (26 + 46 + 56 + 45 + 19 + 22 + 24)/7 = 238/7 = 34

i.e. $\bar{x}$ = 34

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 -10 10

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

$\frac{(8+12+22+11+15+12+10)}{7}=\frac{90}{7}= 12.857$

Therefore, the mean absolute deviation of the given data set is 12.857.

1 Comment

  1. Find the Mean Absolute Deviation (MAD) of the data set: 3, 1, 5, 4, 8, 6. Make sure you write down the mean, distances, and MAD

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