Mean Absolute Deviation Formula

About Mean Absolute Deviation Formula

The average absolute deviation of the collected data set is equal to the sum of absolute deviations from the data set's centre point. Mean absolute deviation, abbreviated as MAD, is made up of four sorts of deviations: central tendency, mean median and mode, and standard deviation. Mean absolute deviation, on the other hand, is the greatest option because it is more accurate and practical in real-world scenarios.

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

mean absolute deviation

Here, xi is Input data values, x? is Mean value for a given set of data,

n is Number of data values

To locate MAD, follow the steps below:

  1. Determine the mean for the given data collection.
  2. Calculate the absolute value of the difference between each value in the data set and the mean.
  3. Calculate the mean absolute deviation by averaging all the absolute values of the difference between the data set and the mean (MAD).

Solved example of Mean Absolute Deviation Formula

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

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

Sol: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. = 34

Now construct the following table for MAD:

Xi Xi-x? |Xi-x?|
26 -8 8
46 12 12
56 22 22
45 11 11
19 -15 15
22 -12 12
24 -10 10

Let's calculate the average of all of the absolute numbers now:

As a result, the data set's mean absolute deviation is 12.857.

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Mean Absolute Deviation Formula

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