Mean Absolute Deviation Calculator

Measure dispersion from mean or median with confidence. Enter lists, weights, or frequencies with ease. See deviations, summaries, charts, exports, and worked examples instantly.

Calculator Input

Enter numbers separated by commas, spaces, semicolons, or new lines.
Leave blank to treat every value as one observation.

Example Data Table

This sample shows a simple raw dataset without separate frequencies.

Observation Value Mean |Value − Mean|
146.82.8
266.80.8
366.80.8
486.81.2
5106.83.2
MAD (2.8 + 0.8 + 0.8 + 1.2 + 3.2) / 5 = 1.76

Formula Used

1) Arithmetic Mean

Mean = Σ(x × f) / Σf

2) Median

Sort the values and locate the point where cumulative frequency reaches half of the total weight.

3) Mean Absolute Deviation

MAD = Σ(f × |x − center|) / Σf

4) Deviation Choice

The calculator lets you measure absolute deviation around either the mean or the median.

Where x is a value, f is frequency or weight, and center is the selected reference point. If no frequencies are entered, every value uses f = 1.

How to Use This Calculator

  1. Enter your dataset in the values box.
  2. Separate numbers with commas, spaces, semicolons, or line breaks.
  3. Add a matching frequency list if your data is summarized.
  4. Select whether deviations should be measured from the mean or median.
  5. Choose how many decimal places you want displayed.
  6. Press the calculate button.
  7. Review the result summary above the form, then inspect the detailed table and graph.
  8. Use the CSV or PDF buttons to export the calculation output.

FAQs

1) What does mean absolute deviation measure?

It measures the average distance between each value and a chosen center. Smaller MAD values show tighter clustering, while larger values show more spread.

2) Why use MAD instead of variance?

MAD stays in the original unit of the data, which makes interpretation easier. Variance uses squared units, so MAD often feels more intuitive.

3) Can I use frequencies instead of raw repeated values?

Yes. Enter one value per position and place its matching frequency or weight in the second box. Both lists must have the same length.

4) Should I calculate deviation from the mean or median?

Use the mean for balanced numeric analysis. Use the median when outliers may distort the center and you want a more resistant reference point.

5) What happens if I leave frequencies blank?

The calculator assumes every value occurs once. That makes it work like a regular raw-data mean absolute deviation tool.

6) Does this tool support decimals and negative numbers?

Yes. You can enter positive, negative, and decimal values. The parser accepts standard numeric formats separated by common delimiters.

7) Is the graph based on absolute deviation values?

Yes. The chart plots each entered item against its absolute deviation from the selected center, helping you see which values contribute most to spread.

8) What export options are included?

You can download a CSV file for spreadsheet work or a PDF file for sharing, reporting, printing, or keeping a calculation record.

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Variance CalculatorMode CalculatorRange CalculatorFive Number SummaryPopulation Mean CalculatorSample Mean CalculatorPopulation Standard DeviationSample Standard DeviationCoefficient of VariationTrimmed Mean Calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.