What Is Mean Absolute Deviation (MAD)?
In statistics, the Mean Absolute Deviation (MAD) is a measure of variability that indicates the average distance between each data point in a set and the mean of that set. In simpler terms, it tells you, on average, how "spread out" your numbers are from the center. A small MAD value means the data points are clustered closely around the mean, indicating low variability. A large MAD value means the data points are spread further apart, indicating high variability. Unlike standard deviation, MAD doesn't square the differences, which makes it less sensitive to outliers and, for some, easier to interpret as a direct average distance.
How to Calculate the MAD: A Step-by-Step Guide
Calculating the MAD is a straightforward three-step process, which our calculator performs and displays for you:
- Find the Mean (Average): First, calculate the mean of the data set by summing all the numbers and dividing by the count of numbers.
- Find the Absolute Deviations: For each number in the data set, calculate the absolute difference between it and the mean. The "absolute" part is key—it means you ignore any negative signs. For example, the absolute difference between 7 and 10 is 3, and the absolute difference between 13 and 10 is also 3.
- Find the Mean of the Deviations: Finally, calculate the mean of all the absolute differences you found in the previous step. This average is the Mean Absolute Deviation.
MAD vs. Standard Deviation
MAD and standard deviation are both measures of data dispersion, but they calculate it differently. While MAD uses the absolute value of the deviations, standard deviation squares the deviations, averages them (the variance), and then takes the square root. This squaring process gives more weight to larger deviations, making standard deviation more sensitive to outliers than MAD.
Because of its simplicity and direct interpretation as an average distance, MAD is often introduced earlier in statistics education. It's an excellent way to grasp the concept of variability before moving on to more complex measures. Many foundational math concepts, like the order of operations, are essential for understanding statistical calculations. For a deeper dive into statistical measures, the Khan Academy has a great review of MAD.