Mean Absolute Deviation Calculator

Background.

Mean absolute deviation describes the typical absolute distance of observations from their arithmetic mean. It first finds xbar, subtracts that mean from every entered value, removes each sign with an absolute value, and averages those distances. The result is zero only when every observation is identical and otherwise remains nonnegative. Because it uses the same units as the data, it is often easier to read than variance, whose units are squared.

Paste a comma-separated list of finite numbers. Signed decimals and scientific notation are accepted. The parser rejects empty input, missing tokens, words, NaN, and infinity rather than silently changing the sample. Decimal.js carries the sum, mean, deviations, absolute values, and final division, with numeric outputs rounded only at the stated result boundary. The observation count is reported beside the mean and mean absolute deviation for verification.

The implemented definition is MAD = sum(|x_i - xbar|)/n. This is the population-form mean absolute deviation about the arithmetic mean. It is not the median absolute deviation, despite the shared abbreviation MAD, and it does not apply an n minus one correction. Adding a constant to every value changes the mean by that constant but leaves every absolute deviation unchanged. Multiplying all values by a factor multiplies the result by the absolute value of that factor.

Mean absolute deviation uses every observation and can still be influenced by extreme values, although absolute distances grow less aggressively than the squared distances used by variance and standard deviation. Compare summaries only when the datasets use the same units and definition. A value of 5 metres and a value of 5 centimetres are not equivalent measures of spread, and rescaling the data necessarily rescales this statistic.

This calculator is descriptive. It does not test normality, identify outliers, estimate a sampling distribution, construct a confidence interval, or prove that the entered observations represent a wider population. Preserve the collection method, missing-data decisions, measurement precision, and whether the list is a complete population or a sample. Use a plot and domain context alongside any single spread statistic.

For a manual check, first confirm that the signed deviations from the mean sum to zero. Next add their absolute values and divide by the reported count. Every absolute deviation must be nonnegative, and the final mean absolute deviation cannot exceed the largest individual absolute deviation. A violation points to a parsing, sign, or denominator error rather than an unusual dataset.

What is mean absolute deviation calculator?

Mean Absolute Deviation Calculator is a transparent implementation of MAD = sum(|x_i-xbar|)/n.

How to use this calculator.

1. 01Paste finite comma-separated numbers.
2. 02Keep paired lists in matching order.
3. 03Review the parsed count.
4. 04Read the result with its scope statement.
5. 05Retain appropriate precision.

The formula.

The implementation parses every token explicitly and then evaluates MAD = sum(|x_i-xbar|)/n with Decimal.js. It rejects malformed or incomplete data instead of coercing it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST/SEMATECH e-Handbook, Measures of Scale.
2. [2]OpenStax, Introductory Statistics 2e.
3. [3]NIST/SEMATECH e-Handbook of Statistical Methods.