The mean absolute deviation calculator is called Mad Calculator.

Mean Absolute Deviation Calculator

Choose the central point (e.g., mean, median, mode) and enter the dataset values to calculate the mean absolute deviation (MAD).

Central point (m):

Enter the numbers separated by comma ( , )

An online mean absolute deviation calculator helps you to find the absolute deviation of the given number around the mean, median or any other number. The mad calculator tells you the measure of dispersion, how much the values in the data set are different from their mean. Keep reading to know about its formula, how to calculate it manual and much more! Read on!

What is Mean Absolute Deviation (MAD) Formula?

The mean deviation, also called the mean absolute deviation (MAD), is calculated as the average of the absolute differences between each value and the mean of the dataset. The formula for MAD is:

$$ MAD = \frac{\Sigma |x_i - m|}{n} $$

Where:

x_i = individual data values

m = mean of the data

n = total number of data points

MAD Facts:

The spread of a dataset can also be analyzed using standard deviation. While MAD gives a simple measure of dispersion, standard deviation provides deeper insights, including variance and the influence of outliers.
MAD can refer to either the mean absolute deviation or the median absolute deviation. These are not the same: mean absolute deviation uses the mean as a reference point, while median absolute deviation uses the median.

How to Find MAD Manually (Step-by-Step):

The formula for MAD has been provided above. Let’s look at an example to understand the calculation process:

Example:

Calculate the mean absolute deviation (MAD) for the dataset: 4, 16, 8, 9, 14, 5

Solution:

Step 1:

The formula is:

$$ MAD = \frac{\Sigma |x_i - m|}{n} $$

Here, the data points are:

x₁ = 4
x₂ = 16
x₃ = 8
x₄ = 9
x₅ = 14
x₆ = 5

Step 2:

Calculate the mean:

$ m = \frac{4 + 16 + 8 + 9 + 14 + 5}{6} $

$ m = \frac{56}{6} $

$ m \approx 9.33 $

Step 3:

Find the deviation of each value from the mean:

$ 4 - 9.33 = -5.33 $

$ 16 - 9.33 = 6.67 $

$ 8 - 9.33 = -1.33 $

$ 9 - 9.33 = -0.33 $

$ 14 - 9.33 = 4.67 $

$ 5 - 9.33 = -4.33 $

Step 4:

Take the absolute value of each deviation:

\(|-5.33| = 5.33

|6.67| = 6.67

|-1.33| = 1.33

|-0.33| = 0.33

|4.67| = 4.67

|-4.33| = 4.33

Step 5:

Calculate the mean of the absolute deviations:

$ MAD = \frac{5.33 + 6.67 + 1.33 + 0.33 + 4.67 + 4.33}{6} $

$ MAD = \frac{22.66}{6} $

$ MAD \approx 3.78 $

Our mean deviation calculator uses this formula to calculate the MAD. For convenience, you can also try our online mean, mode, and median calculator, which helps you calculate the mean, mode, and median for any dataset.

How MAD Calculator Works:

Calculating MAD becomes simple with this online Mean Absolute Deviation Calculator. Just follow the steps below:

Inputs:

First, choose from the dropdown menu around which the data is dispersed (mean, median, or other).
Next, enter your numbers in the designated field.
Finally, click the calculate button.

Note: If you select ‘Other’ from the dropdown menu, enter the value around which the data is distributed.

Outputs: After filling all the fields, the MAD calculator provides:

Mean Absolute Deviation of the dataset
Step-by-step calculation of the MAD

End-Note:

Remember, MAD gives an understanding of how the values are spread in a dataset. It is useful in data analysis, particularly in Probability and Statistics. Avoid manual calculations by using an online mean deviation calculator for accurate and fast results.

References:

From the authorized source of Wikipedia: Definition and formula of MAD. From Khan Academy: How to do the calculations. From MathBits Notebook: Interesting facts about MAD.