# Mean Absolute Deviation Calculator (MAD)

URL: https://speedycalculator.com/calculators/statistics/mad/
Last updated: 2026-10-30

> The mean absolute deviation calculator finds the average distance of your data from a central point – the mean, the median or a value you choose – with a table of every deviation, the steps, and the standard deviation for comparison.

## Inputs

- Data set
- Measure deviations from
- Central value (m)

## Results

- Mean absolute deviation
- Central point used
- Sum of absolute deviations
- Number of values
- Mean
- Population standard deviation (for comparison)
- MAD ÷ standard deviation
- MAD as % of the central point
- Deviation table
- Step-by-step working

## Formula

```
MAD = Σ|xᵢ − m| ÷ n, where m is the mean (default), the median or a chosen value
```

## Explanation

The mean absolute deviation (MAD) answers a very direct question: on average, how far are the values from the centre? Take the distance of each value from the mean, ignore whether it is above or below, and average those distances. If the MAD of daily sales is 3 units, a typical day is about 3 units away from the average day.

Because it uses absolute values rather than squares, the MAD is easy to interpret and less affected by a single large deviation than the standard deviation. For normally distributed data the MAD is about 0.8 times the standard deviation. It is popular in schools as a first measure of spread and in forecasting, where the mean absolute error of predictions is the same idea.

The average distance is smallest when measured from the median, so some texts use the median as the centre. This calculator lets you pick the mean, the median or any value you like, and lists each deviation so you can follow the calculation.

### How to use the Mean Absolute Deviation Calculator

- **Data set**
- **Measure deviations from**
- **Central value (m)**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose the central point m, subtract it from each value, take absolute values, add them up and divide by the number of values.

### Worked example

Nine daily sales: 4, 9, 11, 12, 17, 5, 8, 12, 12. Sum = 90, so the mean is 10. The absolute deviations are 6, 1, 1, 2, 7, 5, 2, 2, 2, which add up to 28. **MAD = 28 ÷ 9 ≈ 3.11**. Measured from the median, 11, the deviations sum to 27 and the MAD is 3.0. The population standard deviation is 3.77, so MAD ÷ SD = 0.82.

### MAD compared with the standard deviation

Squaring makes the standard deviation give extra weight to large deviations; the MAD weighs all deviations equally. A ratio MAD ÷ SD close to 0.8 is typical of normal data; a noticeably lower ratio means a few large deviations dominate the SD – a hint of outliers or heavy tails.

## Worked example

Inputs — Data set: 4, 9, 11, 12, 17, 5, 8, 12, 12; Measure deviations from: The mean.

Results — **Mean absolute deviation = 3.1111**; Central point used = 10; Sum of absolute deviations = 28; Number of values = 9; Mean = 10; Population standard deviation (for comparison) = 3.7712.

## Key terms

- **Absolute deviation**: The distance |x − m| between a value and the central point.
- **Mean absolute deviation**: The average absolute deviation.
- **Central point**: The reference value (mean, median or chosen value) from which deviations are measured.

## FAQ

**How do you calculate the mean absolute deviation?**
Find the mean, subtract it from each value, take absolute values, and average them.

**What is the MAD of 4, 9, 11, 12, 17, 5, 8, 12, 12?**
The mean is 10; the absolute deviations add up to 28, so MAD = 28 ÷ 9 ≈ 3.11.

**What does the mean absolute deviation tell you?**
The typical distance of a value from the centre, in the same units as the data.

**Is MAD the same as the standard deviation?**
No. The SD squares deviations and is always at least as large as the MAD; for normal data MAD ≈ 0.8 × SD.

**Mean absolute deviation or median absolute deviation?**
Both are abbreviated MAD. The mean absolute deviation averages distances from the mean; the median absolute deviation takes the median of distances from the median and is more robust.

**Why measure from the median?**
The sum of absolute deviations is smallest around the median. For the example the MAD about the median (11) is 3.0.

**How do I compute MAD in Excel?**
=AVEDEV(range) gives the mean absolute deviation about the mean.


## Sources

- [Wolfram MathWorld – Mean deviation](https://mathworld.wolfram.com/MeanDeviation.html)
- [Khan Academy – Statistics and probability](https://www.khanacademy.org/math/statistics-probability)
- [NIST/SEMATECH e-Handbook – Measures of scale](https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm)