# Mean Absolute Deviation Calculator (Average Deviation)

## What is the mean absolute deviation?

The mean absolute deviation, also known as average deviation, is a measure of dispersion obtained by calculating the mean of the absolute values of the difference between the observed and expected value of a set of data.

Mathematically it is expressed as follows:

Where:

• Dm: Mean absolute deviation.
• xÌ„: Mean.
• N: Number of evaluated values.
• xi: Each one of the values.

### Mean Absolute Deviation vs. Standard Deviation

Mean absolute deviation, like standard deviation, are measures of dispersion; however, the standard deviation is calculated using the squares of the difference of the observed values from their mean. When squared, it becomes a more sensitive metric to outliers, making it more appropriate than the average deviation for evaluating a data set.

## How to use the average deviation calculator?

The use of the application is straightforward; you only have to follow the following steps:

• Choose between the options for the decimal separator and the data separator.
• Indicate the values of the data set.
• Click on Solve.
• Immediately, you will be able to visualize the calculation procedure step by step.

An example is shown below:

### Example of calculating the mean deviation

For the following data, calculate the mean absolute deviation:

3, 5, 8, 6, 2, 4, 7, 5

#### Solution

We enter the data in the calculator:

When clicking on Solve, we will obtain the following:

Average Deviation: 1.5

Mean: 5

Count of Data: 8

According to the data of the problem we have:

• Î£xáµ¢Â =Â 40
• NÂ =Â 8
• xÌ„Â =Â 40/8 = 5

Finally, we calculate the average deviation:

You can also calculate other measures of dispersion or central tendency using the following options:

## Final Reflection

In short, our mean deviation calculator finds the average of the absolute deviations of the values from the mean in a series of ungrouped data. We are sure it will help you make your homework more accessible and faster.