What Is Mean Absolute Deviation?
The Mean Absolute Deviation (MAD) measures how spread out the values in a data set are. It is the average of the absolute distances between each data point and the mean of the set. Unlike variance or standard deviation, MAD uses absolute values instead of squares, so it is easy to interpret: it tells you, on average, how far each value sits from the center.
How to Use This Calculator
Enter your numbers separated by commas or spaces (for example, 2, 4, 6, 8, 10) and the calculator returns the MAD, the mean, and how many values you entered. There is no limit on data set size, and decimals and negative numbers are both supported.
The Formula Explained
First compute the mean \(\bar{x}\) by adding all values and dividing by the count \(n\). Then, for each value, find the absolute difference from the mean, add those distances together, and divide by \(n\). In symbols: $$\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} \left| x_i - \bar{x} \right|$$ The absolute value ensures positive and negative deviations do not cancel each other out.
Worked Example
For the set 2, 4, 6, 8, 10 the mean is $$\frac{2+4+6+8+10}{5} = 6.$$ The absolute deviations are 4, 2, 0, 2, 4, which sum to 12. Dividing by 5 gives $$\text{MAD} = \frac{12}{5} = 2.4.$$ So values lie an average of 2.4 units from the mean.
FAQ
Is MAD the same as standard deviation? No. Standard deviation squares the deviations before averaging and then takes a square root, which weights outliers more heavily. MAD treats every deviation linearly.
Can MAD be negative? No. Because it averages absolute values, MAD is always zero or positive. It equals zero only when every value is identical.
Which mean does this use? This calculator uses deviations about the arithmetic mean, the most common definition of MAD.
