# Mean Absolute Deviation Calculator

Calculate mean absolute deviation around the mean or median for an easy-to-read spread measure

> Canonical page: https://elysiatools.com/en/tools/mean-absolute-deviation-calculator

- **Category:** Math & Numbers

- **Keywords:** mean absolute deviation, mad, absolute deviation, statistics, spread, median absolute deviation

## Overview

Calculate mean absolute deviation (MAD) for a numeric dataset.

MAD averages absolute distances from a chosen center:

MAD = average(abs(x - center))

Use it when you want a spread measure that is easier to interpret than squared variance and can be centered on either the mean or the median.

## Inputs

- **Dataset** (textarea): e.g. 2, 4, 4, 4, 5, 5, 7, 9
- **Center** (select)
- **Decimal Places** (number)
- **Include Absolute Deviations** (checkbox)

## When to use

- When you need a measure of data dispersion that is easier to explain to non-technical stakeholders than standard deviation.
- When analyzing datasets with extreme outliers where squared variance would disproportionately skew the results.
- When comparing the variability of multiple datasets using either the mean or the median as the central reference point.

## How it works

- Enter your numeric dataset as a comma-separated list into the input field.
- Select your preferred central point for the calculation, choosing between the arithmetic mean or the median.
- Adjust the decimal places and choose whether to include the individual absolute deviations in the final output.
- The tool calculates the center, finds the absolute distance of each number from that center, and averages those distances to output the MAD.

## Use cases

- Evaluating the consistency of manufacturing processes by measuring the average deviation of product dimensions from the target specification.
- Analyzing financial portfolio volatility using a metric that does not over-penalize large, infrequent market swings like standard deviation does.
- Teaching introductory statistics concepts by using an intuitive measure of spread before introducing squared variance.

## Frequently asked questions

### What is the difference between mean absolute deviation and standard deviation?

Mean absolute deviation averages the absolute distances from the center, while standard deviation averages the squared distances and takes the square root. MAD is less sensitive to extreme outliers and often easier to interpret.

### Should I use the mean or the median as the center?

Use the mean for normally distributed data without extreme outliers. Use the median if your dataset is skewed or contains significant outliers, as the median provides a more robust central point.

### How do I format my dataset?

Enter your numbers separated by commas, spaces, or newlines. The tool will automatically parse the numeric values from your input.

### What does the 'Include Absolute Deviations' option do?

When enabled, the JSON output will include an array showing the exact absolute distance of every individual data point from the chosen center, alongside the final mean absolute deviation value.

### Can I adjust the precision of the result?

Yes, you can set the 'Decimal Places' option to round the final mean absolute deviation to your preferred number of decimal digits, up to a maximum of 10.

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