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Mean Absolute Deviation Calculator

Calculate how spread out your data is from the mean or median

Separate values with commas, spaces, or new lines. Minimum 2 values required.

Results

Mean
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MAD
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Count
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# Value (xi) Mean |xi − Mean|

What Is Mean Absolute Deviation?

Mean Absolute Deviation (MAD) is a statistical measure that tells you, on average, how far each data point in your set is from the mean. Unlike standard deviation which squares the differences, MAD uses absolute values – making it simpler to understand and interpret. A smaller MAD means your data points cluster tightly around the mean. A larger MAD indicates greater spread or variability.

Mean Absolute Deviation Formula

The formula for mean absolute deviation is:

MAD = (1/n) × Σ |xi − x̄|

Where:

  • n = the total number of values in your data set
  • xi = each individual value in the data set
  • x̄ = the mean (average) of all values
  • |xi − x̄| = the absolute difference between each value and the mean
  • Σ = summation (add all the absolute differences together)

How to Calculate Mean Absolute Deviation (Step by Step)

Follow these four steps to calculate MAD manually:

Step 1: Find the Mean – Add all values together and divide by the count (n). This gives you x̄.

Step 2: Find Each Deviation – Subtract the mean from each data value: xi − x̄.

Step 3: Take Absolute Values – Remove any negative signs from the deviations: |xi − x̄|.

Step 4: Calculate the MAD – Add all absolute deviations together, then divide by n.

Example - Calculating MAD

Let us calculate the MAD for the data set: 3, 8, 10, 17, 24, 27

  1. Mean = (3 + 8 + 10 + 17 + 24 + 27) ÷ 6 = 89 ÷ 6 = 14.83
  2. Deviations: |3−14.83|=11.83, |8−14.83|=6.83, |10−14.83|=4.83, |17−14.83|=2.17, |24−14.83|=9.17, |27−14.83|=12.17
  3. Sum of absolute deviations = 11.83 + 6.83 + 4.83 + 2.17 + 9.17 + 12.17 = 47.00
  4. MAD = 47.00 ÷ 6 = 7.83

This means each value in the data set differs from the mean by an average of 7.83 units.

MAD vs Standard Deviation - What Is the Difference?

Both MAD and standard deviation measure data spread, but they work differently. Standard deviation squares the differences from the mean, which gives more weight to outliers. MAD uses absolute differences, making it less sensitive to extreme values. MAD is often easier to interpret because it is expressed in the same units as your original data. For most introductory statistics purposes, MAD provides a clear and intuitive measure of variability.

When to Use Mean Absolute Deviation

MAD is useful in many real-world scenarios:

  • Quality control – measuring consistency in manufacturing outputs
  • Finance – analyzing volatility of stock prices or returns
  • Education – understanding grade distribution spread
  • Research – comparing variability across different data sets
  • Weather – measuring temperature deviation from the average

How to Use the KlugWahl Mean Absolute Deviation Calculator

Using our free MAD calculator is simple:

  1. Enter your data values in the input box – separate numbers with commas, spaces, or new lines.
  2. Choose your base: Mean or Median.
  3. Click “Calculate MAD”.
  4. View your results instantly: the mean/median, the MAD value, count, and a full deviation table.

All calculations run in your browser. No data is sent to any server. Your privacy is fully protected.

Frequently Asked Questions

Clear answers regarding calculation fidelity and usage.

A mean absolute deviation calculator is a free online tool that computes the MAD of a data set. It measures how spread out your numbers are from the mean by calculating the average of the absolute differences between each value and the mean. Simply enter your numbers, and the calculator gives you the MAD value instantly with step-by-step results.
To calculate mean absolute deviation: (1) Find the mean of your data set by adding all values and dividing by the count. (2) Subtract the mean from each value and take the absolute value. (3) Add all absolute deviations together. (4) Divide by the number of values. The formula is MAD = (1/n) × Σ |xi − x̄|.
Mean Absolute Deviation (MAD) uses absolute differences from the mean, while standard deviation uses squared differences. MAD is simpler to interpret and less sensitive to outliers. Standard deviation gives more weight to extreme values. Both measure data spread, but MAD is often more intuitive for beginners and real-world applications.
Yes. Some calculations use the median as the central point instead of the mean - this is called Median Absolute Deviation. The KlugWahl calculator lets you choose between Mean and Median as your base. Median-based MAD is more robust against outliers and is commonly used in advanced statistics and machine learning applications.
A low MAD means your data points are close to the mean - the data is consistent and has low variability. A high MAD means data points are spread far from the mean - the data is more variable. For example, a MAD of 2 in test scores means students typically scored within 2 points of the average, indicating very consistent performance.
Yes. The KlugWahl mean absolute deviation calculator is 100% free with no sign-up required. All calculations run entirely in your browser using client-side JavaScript. No data is ever sent to our servers. Your numbers never leave your device, ensuring complete privacy.