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Free Online Mean Absolute Deviation Calculator, MAD Around Mean or Median

Work out the mean absolute deviation of a list of numbers, around the mean or around the median. Every individual distance is listed so the answer can be checked by hand, and the standard deviation is shown alongside, because the two measure the same idea and disagree in a way worth understanding.

Free Forever Nothing Uploaded Mean or Median Every Distance Listed

Free Online Mean Absolute Deviation Calculator, MAD Around Mean or Median

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📊 Mean Absolute Deviation Calculator Around the mean or the median · every distance listed

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Measure the distances from

How many numbers 0

📊 Your numbers

Separated by commas, spaces, semicolons or new lines. A column pasted straight out of a spreadsheet works as it is.

Numbers

Try one of these

The second and fifth show what one distant value does to each measure.

Mean absolute deviation

—

The centre used—

Total of the distances—

MAD around the mean—

MAD around the median—

Standard deviation, sample—

SD divided by MAD—

Each number, how far it is from the centre, and the running total. This is the whole calculation, so it can be checked by hand.

#	Value	Distance from the centre	Running total

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How to Work Out the Mean Absolute Deviation

Three steps, and the second is a real choice rather than a formality.

Paste the numbers Commas, spaces, semicolons or new lines all work, so a column copied out of a spreadsheet needs no tidying first.

Choose the mean or the median as the centre Both answers are shown either way, but the one you choose is the one reported at the top. The median always gives a smaller or equal answer, which is a mathematical fact rather than a quirk of your data.

Open the list of distances to check it Every value, its distance from the centre and the running total. The mean absolute deviation is simply that total divided by how many numbers there are, and seeing the list makes that obvious.

What to Know About Absolute Deviation

Why the median gives a smaller answer, and when to prefer it.

The median always gives a smaller answer, and that is not a coincidence. The median is defined by exactly this property: it is the point that makes the total of the absolute distances as small as it can be. So the mean absolute deviation around the median is always less than or equal to the one around the mean, and equal only when the two centres coincide. Both are shown here so the gap is visible, and on skewed data the gap is large.

This is not the standard deviation, and the difference is the point. Both measure spread. The standard deviation squares each distance before averaging, which gives distant values far more weight; absolute deviation does not square, so it treats a value ten away as ten times a value one away rather than a hundred times. On a normal distribution the standard deviation comes out about 1.2533 times the mean absolute deviation, and a ratio much larger than that is a sign that something distant is pulling at your data.

MAD also means median absolute deviation, which is a different thing again. The same three letters are used for the median of the absolute distances, usually from the median, which is a robust measure used in outlier detection. This page calculates the mean of the absolute distances, which is what is taught at school under this name. Both are legitimate, they are not equal, and the abbreviation does not distinguish them, so the full name is written out everywhere here.

There is no sample and population distinction here. Standard deviation has two versions, dividing by n or by n minus one, because squaring introduces a bias that the correction removes. Absolute deviation has no such correction in common use, so it is always divided by n. If you were expecting to choose, that is why there is no switch.

All identical values give zero, which is the right answer. If every number is the same, every distance is zero and so is the deviation. That is not an error or a missing result: it is the statement that the data has no spread at all. Two values always give a mean absolute deviation of exactly half the gap between them, which is a quick way to sanity check the arithmetic.

Your numbers stay in this tab. Everything is worked out in the page, so a column of real figures pasted out of a spreadsheet is not uploaded anywhere, and the page keeps working with the network off.

Key Features & Capabilities

What it does, and what it deliberately does not.

Mean and median both Both centres worked out every time, with the one you chose reported and the other shown for comparison.

Every distance listed Value, distance and running total, so the answer can be checked by hand rather than taken on trust.

Standard deviation alongside And the ratio between them, which is about 1.2533 on well behaved data and larger when an outlier is present.

Paste a spreadsheet column Commas, spaces, semicolons and new lines are all accepted, and anything unreadable is named rather than skipped.

Says which MAD it means The abbreviation covers two different measures, so the full name is written out rather than left ambiguous.

Nothing is uploaded It runs in this tab and keeps working offline.

About Mean Absolute Deviation

The mean absolute deviation answers a question anyone can state: on average, how far from the middle is a typical value? Work out the middle, measure how far each number is from it, ignore whether that distance is up or down, and average those distances. There is nothing hidden in it, which is exactly why it is taught before the standard deviation.

The interesting decision is which middle. Almost every calculator uses the mean without mentioning that the median is an option, and the choice matters more than it sounds. The median is characterised by this very property: it is the point that minimises the total absolute distance. So the deviation around the median is always smaller than or equal to the deviation around the mean, and on skewed data it is much smaller. On the list one, two, three, four, a hundred the two answers are a long way apart, and the one around the median is the better description of where the data actually sits.

The second thing worth understanding is how this relates to the standard deviation, since both claim to measure spread. The standard deviation squares every distance before averaging and then takes a square root, and squaring is not a neutral act: a value ten units away contributes a hundred rather than ten, so distant values dominate. Absolute deviation gives every unit of distance the same weight. On data that follows a normal distribution the standard deviation works out at about 1.2533 times the mean absolute deviation, so that ratio is a useful diagnostic. If it is much larger, something far from the middle is doing most of the work.

The practical upshot is that neither is better in general and they answer slightly different questions. If you want a number that behaves well in further algebra, the standard deviation is the one, which is most of the reason it won. If you want a number that describes a typical distance without being hijacked by one unusual value, this is the one. Showing both, with the ratio, is more useful than arguing for either.

Frequently Asked Questions

Mean or median, the difference from standard deviation, and outliers.

The mean is the usual school answer and what most textbook questions expect. The median gives a smaller answer and describes typical data better when the list is skewed or has an unusual value in it. Both are shown, so you can see how much difference it makes to your numbers.

Because that is the defining property of the median: it is the point that makes the total of the absolute distances as small as possible. Any other centre, including the mean, gives a total that is larger or at best equal.

The standard deviation squares each distance before averaging, which gives far more weight to values a long way from the middle. Absolute deviation does not square, so one extreme value moves it much less. On normal data the standard deviation is about 1.2533 times the mean absolute deviation.

No. Dividing by n minus one corrects a bias that comes from squaring, and absolute deviation does not square, so there is no accepted correction and it is always divided by n. That is why there is no switch for it here.

It is used for both mean absolute deviation and median absolute deviation, which are different measures. This page works out the mean of the absolute distances. The median of those distances is a separate, more robust statistic used in outlier detection.

The answer is zero, which is correct: there is no spread at all. With exactly two numbers the mean absolute deviation is always half the gap between them, which is a useful way to check the arithmetic.

No. The whole calculation happens in your browser, so a column of real figures pasted from a spreadsheet stays in the tab and the page works offline once loaded.