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Median Absolute Deviation Calculator

Paste a list of numbers to calculate median absolute deviation around the median. The sorted values and each absolute deviation stay visible, so robust spread can be checked instead of treated as a black box.

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|. The robust statistic: one wild value moves it hardly at all, which is why outlier rules are built on it.

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. One wild value drags the first a long way and moves the second hardly at all. 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.
Accuracy. Exact arithmetic: the mean of the absolute deviations from the centre you choose, with every deviation shown so you can add them up yourself. Mean deviation about the mean and median absolute deviation about the median are two different statistics and are labelled separately here, never merged. The 1.4826 normal-consistency scaling is an approximation and is shown apart from the raw value.

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, making it less sensitive to outliers than standard deviation.

Exact arithmetic: the mean of the absolute deviations from the centre you choose, with every deviation shown so you can add them up yourself. Mean deviation about the mean and median absolute deviation about the median are two different statistics and are labelled separately here, never merged. The 1.4826 normal-consistency scaling is an approximation and is shown apart from the raw value.