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# Mean Absolute Deviation Calculator

## 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.

## Other Calculators

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:

• 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