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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 ( , )

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The online Mean Absolute Deviation (MAD) calculator helps you quickly measure the dispersion of a dataset. It computes how far each value in the dataset deviates from the mean, median, or any specified number, providing a clear understanding of data variability. Keep reading to learn the formula, manual calculation steps, and more!

What is Mean Absolute Deviation (MAD)?

Mean Absolute Deviation (MAD) is the average of the absolute differences between each data point and a chosen central value (usually the mean or median). The formula for MAD is:

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

Where:

x_i = individual data values
c = central value (mean, median, or chosen number)
n = total number of data points

Key Facts About MAD:

MAD provides a simple measure of spread, while standard deviation gives more detailed insights including variance and the effect of outliers.
MAD can be calculated with respect to either the mean (mean absolute deviation) or the median (median absolute deviation). They are similar but not the same.

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

Let’s go through an example to understand MAD calculation:

Example:

Find the MAD for the dataset: 6, 12, 8, 10, 14, 4

Solution:

Step 1: Identify the data points:

x₁ = 6
x₂ = 12
x₃ = 8
x₄ = 10
x₅ = 14
x₆ = 4

Step 2: Calculate the mean:

$ m = \frac{6 + 12 + 8 + 10 + 14 + 4}{6} = \frac{54}{6} = 9 $

Step 3: Determine deviations from the mean:

6 - 9 = -3

12 - 9 = 3

8 - 9 = -1

10 - 9 = 1

14 - 9 = 5

4 - 9 = -5

Step 4: Take the absolute value of each deviation:

|-3| = 3, |3| = 3, |-1| = 1, |1| = 1, |5| = 5, |-5| = 5

Step 5: Compute the mean of absolute deviations:

$ MAD = \frac{3 + 3 + 1 + 1 + 5 + 5}{6} = \frac{18}{6} = 3 $

Thus, the mean absolute deviation of the dataset is 3.

For convenience, you can also use our online mean, median, and mode calculator to quickly find the central values before calculating MAD.

How the MAD Calculator Works:

The online MAD calculator simplifies the process. Follow these steps:

Inputs:

Select the reference point for deviations (mean, median, or other value).
Enter the dataset into the input field.
Click the "Calculate" button.

Note: If you select 'Other', enter the specific value around which deviations are measured.

Outputs:

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

Conclusion:

MAD is a valuable tool for understanding data spread. It provides a clear measure of variability and is especially useful in statistics and probability. Using an online MAD calculator saves time and ensures accuracy compared to manual calculations.

References:

Wikipedia: Mean Absolute Deviation. Khan Academy: MAD Calculation Guide. MathBits Notebook: Facts about MAD.

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