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How to Find Average Deviation

Published in Data Analysis 2 mins read

Average deviation, also known as mean absolute deviation (MAD), measures the average distance between each data point and the mean (average) of the dataset. It provides a simple way to understand the spread or dispersion of data.

Calculating Average Deviation: A Step-by-Step Guide

  1. Calculate the Mean: Find the average of your dataset by summing all values and dividing by the total number of values. Indeed.com explains this initial step clearly. For example, for the dataset {2, 4, 6, 8}, the mean is (2+4+6+8)/4 = 5.

  2. Find the Absolute Deviations: Subtract the mean from each data point. Then, take the absolute value (ignore negative signs) of each difference. This gives you the absolute deviation of each data point from the mean. Statisticshowto.com highlights the importance of using absolute values. For our example:

    • |2 - 5| = 3
    • |4 - 5| = 1
    • |6 - 5| = 1
    • |8 - 5| = 3

  3. Calculate the Average Deviation: Sum all the absolute deviations calculated in step 2. Then, divide this sum by the total number of values in your dataset. This final result is your average deviation. As stated in the provided text from July 30, 2024, you "add them all together and divide them by the total number of values in the data set". For our example: (3 + 1 + 1 + 3) / 4 = 2. The average deviation is 2.

Understanding Average Deviation

  • Simplicity: Average deviation is easy to understand and calculate, making it a useful measure for quickly assessing data spread.
  • Sensitivity to Outliers: While simple, average deviation is sensitive to outliers (extreme values). Outliers can significantly inflate the average deviation.
  • Alternative to Standard Deviation: While similar in purpose, average deviation differs from standard deviation, which uses squared deviations, making it less sensitive to outliers but more complex to calculate. Investopedia provides a comparison between these two measures.

Example using a different dataset:

Let's consider the dataset {10, 12, 15, 18, 20}.

  1. Mean: (10 + 12 + 15 + 18 + 20) / 5 = 15

  2. Absolute Deviations:

    • |10 - 15| = 5
    • |12 - 15| = 3
    • |15 - 15| = 0
    • |18 - 15| = 3
    • |20 - 15| = 5

  3. Average Deviation: (5 + 3 + 0 + 3 + 5) / 5 = 3.2

Therefore, the average deviation for this dataset is 3.2.

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