Mean Absolute Deviation Calculator
The Mean Absolute Deviation Calculator quickly measures average distance of data points from the mean, providing clear insights into variability and consistency.
1,2,3,4,5 or each on new lines. Supports Math.js: 2^3, sqrt(2)+1, ranges 1:5. Any matrices/ranges will be flattened.Results
MAD(x) = mean(abs(x - mean(x)))x = [1,2,3,4,5]; MAD = mean(abs(x - mean(x)))Helping notes
- Enter values as a list, separated by commas or new lines. Expressions are supported and evaluated with Math.js.
- MAD is computed as
mean(abs(x - mean(x)))(about the mean). - Decimal places affect displayed results only; internal math uses full precision.
What is a Mean Absolute Deviation (MAD) Calculator?
A Mean Absolute Deviation (MAD) calculator automates a simple but powerful statistical idea: measure how far, on average, your data points lie from their mean. By converting differences to absolute values, MAD expresses variability in the original units of your data, making it intuitive for quality control, classrooms, surveys, business metrics, and everyday analysis. Compared with variance or standard deviation, MAD is robust to occasional extreme values and easier to interpret at a glance. When you enter a list of numbers, this tool computes the sample mean and then averages the absolute distances from that mean to deliver a single, easy-to-understand measure of spread.
About the Mean Absolute Deviation Calculator
This calculator uses math.js for precise numeric operations and MathJax for crisp, responsive formulas on any screen size. It accepts comma-, space-, or newline-separated values and gracefully ignores blanks or stray text. The output panel reports the number of observations (n), the arithmetic mean ($\\bar{x}$), and the computed MAD. Because MAD averages absolute distances from the mean, it remains interpretable in the same units as your data—milliseconds, dollars, centimeters, or scores—so you can immediately compare variability across datasets. The interface is lightweight, mobile-friendly, and suited for embedding within reports, dashboards, or learning portals.
How to Use this Mean Absolute Deviation Calculator
- Paste or type your numbers into the input box. Separate values with commas, spaces, or line breaks.
- Click Calculate MAD. The tool computes the mean $\\bar{x}$ and then averages absolute distances to return MAD.
- Read the results: larger MAD implies greater average spread around the mean; smaller MAD implies tighter clustering.
- Use MAD to compare consistency across teams, experiments, or time periods without converting units.
Note: This tool computes the mean-based MAD (not the median-based “median absolute deviation”). For teaching, both are valuable measures of variability.