# Mean Absolute Deviation Calculator

Calculate Mean Absolute Deviation from your data. See the average distance from the mean with step-by-step individual deviations and interpretation.

## What this calculates

Calculate the Mean Absolute Deviation (MAD) from up to 10 data values. MAD measures the average distance of data points from the mean, providing a simple and intuitive measure of spread.

## Inputs

- **Number of Values** — min 2, max 10 — How many values to analyze (2-10).
- **Value 1** — Data point 1.
- **Value 2** — Data point 2.
- **Value 3** — Data point 3.
- **Value 4** — Data point 4.
- **Value 5** — Data point 5.
- **Value 6** — Data point 6.
- **Value 7** — Data point 7.
- **Value 8** — Data point 8.
- **Value 9** — Data point 9.
- **Value 10** — Data point 10.

## Outputs

- **Mean Absolute Deviation** — Average absolute distance from the mean.
- **Mean** — Arithmetic mean of the data.
- **Individual Deviations** — formatted as text — Absolute deviation of each value from the mean.
- **Interpretation** — formatted as text — What the MAD value means for your data.

## Details

Mean Absolute Deviation is a measure of variability that describes how spread out data values are from the arithmetic mean. Unlike variance and standard deviation, MAD uses absolute values instead of squaring, making it easier to interpret.

Formula: MAD = (1/n) x sum of |xi - mean| for all i. You first calculate the mean, then find the absolute difference between each data point and the mean, and finally average those absolute differences.

MAD vs. Standard Deviation: Both measure spread, but MAD is less sensitive to outliers because it does not square deviations. For a normal distribution, the standard deviation is approximately 1.2533 times the MAD. MAD is preferred when communicating results to non-technical audiences because it has a clear interpretation: the average distance from the average.

## Frequently Asked Questions

**Q: What is the difference between MAD and standard deviation?**

A: MAD uses absolute differences from the mean, while standard deviation squares the differences. Standard deviation gives more weight to outliers (large deviations are squared). MAD is more robust and easier to interpret, but standard deviation is more common in statistical formulas because squared values have nicer mathematical properties.

**Q: Can MAD be zero?**

A: Yes, MAD is zero when all data values are identical (equal to the mean). A MAD of zero means there is no variability at all in the data.

**Q: When should I use MAD instead of standard deviation?**

A: Use MAD when your data has outliers, when you want a robust measure of spread, or when you need to communicate variability to a general audience. Standard deviation is preferred for statistical inference, hypothesis testing, and when data is approximately normally distributed.

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Source: https://vastcalc.com/calculators/statistics/mean-absolute-deviation
Category: Statistics
Last updated: 2026-04-21