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Mean Absolute Deviation Calculator


  • Mean Absolute Deviation

How does Mean Absolute Deviation Calculator work?

  • Enter the data set (x) In The Input Box.
  • Hit The Calculate Button.
  • Use The Reset Button To calculate New Values.




Mean absolute deviation calculator is used to find the absolute deviation of the given set of data. This tool also provides sample size, mean, and absolute difference sum.


What is the mean absolute deviation?


The mean absolute deviation of a dataset is the average distance between each data point and the mean. The idea of variability in a dataset can be taken from it.


Mean absolute deviation formula:


The general formula of mean absolute deviation is:

mean absolute deviation formula

  • m(X) is the mean of the dataset.
  • xi are the data values.
  • n is the total number of terms in a dataset.
  • |xi – m(X)| is the absolute deviation

How to calculate the mean absolute deviation?


Below is a solved example of mean absolute deviation.

Example:

Find the mean absolute deviation of the given set of data
12, 14, 18, 24, 26, 32

Solution:

Step 1: Evaluate the mean.
Mean = x̅ = (12 + 14 + 18 + 24 + 26 + 32)/6
Mean = x̅ = 126/6
Mean = x̅ = 21

Step 2: Calculate the absolute deviation and add those deviations together.

xi xi - x̅ | xi - x̅ |
12 12 – 21 = -9 |-9| = 9
14 14 – 21 = -7 |-7| = 7
18 18 – 21 = -3 |-3| = 3
24 24 – 21 = 3 |3| = 3
26 26 – 21 = 5 |5| = 5
32 32 – 21 = 11 |11| = 11
    Σ| xi - x̅ | = 38

Step 3: To get the mean absolute deviation, divide the sum of the mean deviation by the total number of data values.
MAD = Σ| xi - x̅ | / n
MAD = 38/2
MAD = 19


References:


Khan Academy. (n.d.). What is the mean absolute deviation? | Khan Academy
Formula & example of MAD | Study.com | Take Online Courses. Earn College Credit.