Median Absolute Deviation Calculator

In statistics, deviation means the difference between an observed value and a statistically significant central point. You measure it to see how spread out the points of a dataset are. In a set that can be characterized by the normal distribution, we recommend using standard deviation. For non-normal data, you can use median absolute deviation.

But what are absolute deviation and median?

• Absolute deviation means that it doesn't matter if a number is bigger or smaller than the central point — the distance between them is always positive.
• Median is the "middle" number of a sorted set. It always has the same amount of numbers below and above it. In a dataset containing an even amount of numbers, the median is the average between the two middlemost numbers.

By calculating the median absolute deviation, also known by its acronym MAD, you determine the median of the positive deviations around the median. Somewhat confusing? We'll look at the formula and a step-by-step solution in a second.

💡 The acronym MAD is also used to describe mean absolute deviation. It's similar in concept, but not the same. Learn more about it in the mean absolute deviation calculator.

The median absolute deviation formula is:

MAD = median(X_i - m), where

• m is the median of a dataset; and
• X_i is the dataset in question.

You calculate median absolute deviation around the median. Here's how to do that in a few steps:

1. Sort the dataset and find the median. (Learn how to do that in our median calculator).

2. Subtract the median from each data point.

3. Find the absolute value of each number.

4. Sort the numbers.

5. Find the median of the new dataset.

Let's use these five steps to solve a MAD exercise.

Let's say you organized a running race between you and some of your friends. You all ran 100 m and wrote down your results: 12s, 16s, 12s, 11s, 14s, 15s. How to calculate the median absolute deviation of your running times?

1. First, sort the dataset, [11, 12, 12, 14, 15, 16], and find the median. m = 13

2. Get the new dataset by subtracting the median from each data point:

• 11 - 13 = -2
• 12 - 13 = -1
• 12 - 13 = -1
• 14 - 13 = 1
• 15 - 13 = 2
• 16 - 13 = 3

3. Find the absolute value of each point:

• |-2| = 2
• |-1| = 1
• |-1| = 1
• |1| = 1
• |2| = 2
• |3| = 3

4. Sort new points: [1, 1, 1, 2, 2, 3]
5. Find the median: MAD = 1.5

Before you go, learn more about deviation and other ways of analyzing a dataset with the mean median mode calculator and the variance calculator.