Median Absolute Deviation (MAD)
Compute the median absolute deviation (MAD) of any dataset — a robust measure of statistical dispersion around the median. Free online calculator with step-by-step absolute deviations, charts, and summary statistics.
About This Calculator
The Median Absolute Deviation (MAD) Calculator computes a robust measure of statistical dispersion that tells you how spread out your data is around the median. Unlike standard deviation — which is sensitive to outliers because it uses the mean and squares deviations — MAD uses the median and absolute deviations, making it resistant to extreme values and ideal for non-normal or skewed distributions.
This calculator is useful for students learning descriptive statistics, data analysts evaluating the spread of non-normal datasets, researchers performing robust statistical analyses, and anyone working with data that may contain outliers. The MAD is particularly valuable in fields like finance (for analyzing volatile asset returns), quality control, and environmental monitoring where extreme values are common and shouldn't overly influence the dispersion measure.
How the Calculation Works
The formula for median absolute deviation is MAD = median(|Xᵢ - m|), where m is the median of your dataset. The calculator performs these steps: (1) sorts your data and finds the median, (2) subtracts the median from each value, (3) takes the absolute value of each difference, (4) sorts the absolute deviations, and (5) finds the median of those sorted deviations. The result — the MAD — represents the typical distance of a data point from the median.
The results panel also shows the dataset median, mean, and count alongside the MAD value. The bar chart visualizes the absolute deviations from the median for each data point, while the line chart shows the sorted data distribution.
Regional Notes
Median absolute deviation is a universal statistical concept used identically across all regions (India, US, UK, and worldwide). No region-specific conventions apply. The results use numerical formatting compatible with all locales.
Frequently Asked Questions
What is median absolute deviation (MAD)?
Median absolute deviation (MAD) is a robust measure of statistical dispersion that measures the variability of a dataset. It is calculated as the median of the absolute deviations from the dataset's median. Unlike standard deviation, MAD is not influenced by outliers, making it ideal for non-normal distributions.
How is median absolute deviation calculated?
To calculate MAD: 1) Find the median of the dataset. 2) Subtract the median from each data point. 3) Take the absolute value of each difference. 4) Sort these absolute deviations. 5) Find the median of this new set of values. The result is the median absolute deviation.
What is the difference between MAD and standard deviation?
MAD uses the median as the central point and takes the median of absolute deviations, making it robust to outliers. Standard deviation uses the mean and squares the deviations, so it is sensitive to extreme values. MAD is preferred for non-normal or skewed distributions, while standard deviation is optimal for normally distributed data.
When should I use median absolute deviation instead of mean absolute deviation?
Use median absolute deviation when your data contains outliers or follows a non-normal distribution. The median is less sensitive to extreme values than the mean, so MAD provides a more reliable measure of spread for skewed datasets. Mean absolute deviation is better suited for symmetric distributions without outliers.
Can MAD be zero?
Yes, MAD can be zero if all values in the dataset are identical. For example, if every data point is 5, the median is 5, all absolute deviations are 0, and the median of those zeros is 0. A MAD of zero indicates no variability in the data.
What is a good median absolute deviation value?
There is no universal "good" MAD value — it depends entirely on the scale of your data. A MAD of 5 means the typical data point is 5 units away from the median. To interpret spread relative to scale, divide MAD by the median to get the relative MAD. For comparing datasets, always compare MAD values within the same unit and context.
How does MAD relate to outlier detection?
MAD is commonly used in robust outlier detection methods. A common rule is to flag data points as outliers if they fall more than 3 MADs away from the median (for normally distributed data) or 2.5 MADs for general purpose use. This is more robust than the standard deviation-based Z-score method.
What is the formula for median absolute deviation?
The formula for median absolute deviation is MAD = median(|Xᵢ - m|), where m is the median of the dataset and Xᵢ represents each data point. The vertical bars denote absolute value, meaning all deviations are treated as positive distances from the median.