Mean Absolute Deviation Calculator

Calculate mean absolute deviation

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About Mean Absolute Deviation Calculator

A Mean Absolute Deviation (MAD) calculator that computes the average distance of data points from the mean. Shows individual absolute deviations, step-by-step calculation, and compares MAD to standard deviation. Includes a visual spread indicator. All processing is client-side. Essential for statistics students and anyone analyzing data variability with an intuitive measure of spread.

Mean Absolute Deviation Calculator Features

  • Step-by-step
  • Individual deviations
  • SD comparison
  • Visual spread
  • Population & sample
Mean Absolute Deviation (MAD) measures data spread by averaging the absolute distances from the mean. MAD = Σ|xᵢ − x̄| / n. Unlike standard deviation, MAD doesn't square differences, making it more intuitive: it literally tells you 'on average, how far values are from the mean.'

How to Use

Enter your data:

  • Input: Comma or space-separated numbers
  • MAD: Average absolute deviation computed
  • Comparison: See how it compares to SD

The Formula

  • MAD = Σ|xᵢ − x̄| / n
  • 1. Calculate the mean (x̄)
  • 2. Find |each value − mean|
  • 3. Average those absolute differences

MAD vs Standard Deviation

MAD is simpler and more robust to outliers. SD penalizes large deviations more (squaring). For normal data, SD ≈ 1.25 × MAD. MAD is preferred in some fields like finance.

Step-by-Step Instructions

  1. 1Enter numbers separated by commas.
  2. 2View the computed MAD.
  3. 3Check individual deviations.
  4. 4Compare MAD to standard deviation.
  5. 5Review the step-by-step calculation.

Mean Absolute Deviation Calculator — Frequently Asked Questions

Why use MAD instead of standard deviation?+

MAD is more intuitive (literal average distance) and more robust to outliers. SD squares differences, so one extreme value has outsized impact. MAD treats all deviations equally.

How do I interpret MAD?+

MAD tells you the average distance from the mean. MAD=5 means 'on average, values are 5 units from the mean.' Lower MAD = less spread, higher MAD = more spread.

What's the relationship between MAD and SD?+

For normally distributed data, SD ≈ 1.2533 × MAD. For uniform distributions, the relationship differs. SD is always ≥ MAD.

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