What does median absolute deviation measure?

It takes the median of the absolute distances from each value to the data set's median. Median-based spread is less sensitive to extremes in many lists; the effect depends on the list size and distribution.

Median Absolute Deviation Calculator

Calculate median absolute deviation about the median. This page opens with Median about the median selected and shows the sorted values, sorted absolute deviations and their median. The raw value and its approximate 1.4826 scaling appear separately.

8 valuesCentre: medianMedian absolute deviation

values sorted    2  4  4  4  5  5  7  9        n = 8
median           (4 + 5) / 2  =  4.5

|x - 4.5| sorted 0.5  0.5  0.5  0.5  0.5  2.5  2.5  4.5        sum = 12

median absolute deviation about the median   (0.5 + 0.5) / 2  =  0.5
scaled           1.4826 x 0.5  =  0.7413        an approximation

n: 8
Centre (median): 4.5
Scaled by 1.4826: 0.7413
Median absolute deviation: 0.5

Which statistic

Median absolute deviation about the median. Take the median of every |x - median|. Median-based spread is less sensitive to extremes in many lists; the effect depends on the list size and distribution.

Your numbers

Median absolute deviation about the median of 8 values is 0.5.

Commas, spaces, tabs, semicolons and new lines all separate values, so a column copied from a spreadsheet pastes straight in, and up to 10,000 values are read at a time. Figures on screen are rounded to six decimal places; the arithmetic itself keeps full double precision. Nothing you type leaves this browser.

Worked examples

1, 2, 3centre is the mean, 2
Mean absolute deviation 0.666667, the sum 2 over n 3.
A single valuen = 1
Mean absolute deviation 0: the only value is the centre, so every deviation is zero.
1, 2, 100 about the medianmedian absolute deviation
Median absolute deviation 1, scaled 1.4826, where the mean absolute deviation about the mean is 43.777778.

Two statistics, one abbreviation. MAD is written for both the mean of the absolute deviations and the median of the absolute deviations, and they are different numbers: on 1, 2, 100 the mean absolute deviation about the mean is 43.777778 and the median absolute deviation about the median is 1. Median-based spread is less sensitive to extremes in many lists; the effect depends on the list size and distribution. This page computes whichever you pick and labels it by its full name rather than by the abbreviation.

About the 1.4826 scaling. Scaling by 1.4826 makes a median absolute deviation comparable to a standard deviation, but only when the data is normal. The factor is 1 divided by the standard normal's 0.75 quantile, 1.482602218505602, rounded: it is an approximation, so the raw value is the one to quote unless you want that comparison.

Common questions

What does median absolute deviation measure?: It takes the median of the absolute distances from each value to the data set's median. Median-based spread is less sensitive to extremes in many lists; the effect depends on the list size and distribution.

Exact arithmetic formulas are evaluated with double-precision numbers; displayed values are rounded to six decimal places, or shown in scientific notation for very small or large values. Mean absolute deviation and median absolute deviation are labelled separately, with every deviation shown. The 1.4826 normal-consistency scaling is an approximation shown apart from the raw median absolute deviation.