Median Absolute Deviation Calculator

Use this median absolute deviation calculator to measure how much your data spread out from the median and find outliers. It finds the absolute median distance that data points fall from the median and values that are unusual far from the median. Just enter or paste your numbers in the data box, separated by commas, spaces, or line breaks. You can copy and paste from spreadsheets. Then click Calculate to see how much the values in your dataset differ from the median.

The calculator will show you the median absolute deviation (MADM), median, count, and a histogram of your data. Optionally, it can use the MADM to find outliers. Use this tool to quickly understand the median distance between your data points and the sample median. Below the calculator is additional information about how to interpret and use it. Related: Standard Deviation Calculator and Mean Absolute Deviation Calculator. See all my Statistical Calculators!

For more information about interpreting the results and the calculation methods for this median absolute deviation calculator, please read my article about MADM: Definition, Finding & Formula.

In addition to using MADM as a measure of variability, researchers can use this median absolute deviation calculator as a practical tool for detecting outliers. Leys et al. (2013) recommend identifying outliers as values that fall outside the range of the median plus or minus 2.5 times the MADM. They show that the common mean ± SD rule and Z-score approaches can completely miss obvious outliers because both the mean and standard deviation are distorted by extreme values. In contrast, the MADM-based rule resists those distortions and gives a clearer boundary, allowing analysts to detect truly unusual values even in small or skewed samples. Learn more about 5 Ways to Find Outliers or use my Outlier Test Calculator for additional methods.

Reference

Leys, C., Ley, C., Klein, O., Bernard, P., & Licata, L. (2013). Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology, 49(4), 764–766. https://doi.org/10.1016/j.jesp.2013.03.013