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How to Find the Absolute Deviation?

Published in Statistics 2 mins read

To find the absolute deviation (more specifically, the mean absolute deviation), follow these steps:

  1. Calculate the Mean: Determine the average of your dataset. This is done by summing all the values in the dataset and dividing by the number of values.

  2. Calculate the Absolute Deviations: For each number in the dataset, subtract the mean you calculated in step 1. Then, take the absolute value of the result. The absolute value of a number is its distance from zero, meaning you ignore the sign (positive or negative).

  3. Sum the Absolute Deviations: Add up all the absolute deviations you calculated in step 2.

  4. Calculate the Mean Absolute Deviation (MAD): Divide the sum of the absolute deviations (from step 3) by the total number of values in your original dataset. This final result is the mean absolute deviation.

In Summary:

The mean absolute deviation is calculated as follows:

MAD = (Sum of |value - mean|) / (Total number of values)

Example:

Let's say our dataset is: 2, 4, 6, 8, 10

  1. Mean: (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6

  2. Absolute Deviations:

    • |2 - 6| = 4
    • |4 - 6| = 2
    • |6 - 6| = 0
    • |8 - 6| = 2
    • |10 - 6| = 4

  3. Sum of Absolute Deviations: 4 + 2 + 0 + 2 + 4 = 12

  4. Mean Absolute Deviation (MAD): 12 / 5 = 2.4

Therefore, the mean absolute deviation of the dataset 2, 4, 6, 8, 10 is 2.4.

Why is Mean Absolute Deviation Useful?

The mean absolute deviation provides a measure of the average distance each data point is from the mean of the dataset. It gives you a sense of the data's variability. A smaller MAD indicates data points are clustered closer to the mean, while a larger MAD indicates they are more spread out.

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