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Absolute Deviation Calculator

Calculate average absolute deviation from mean or median to measure data spread

Calculate Deviation

Separate values with commas, spaces, or semicolons Use a dot for decimals (1.5); commas separate values, not decimal digits.

Method and source check

Last checked:

Automated source and implementation review, including worked examples and documented numerical limits. This review does not provide professional advice or specialist approval.

Method

Compute arithmetic mean and median, select one as the center, average absolute distances from that center, and also report their sum. Median-centered mode still averages distances; it does not compute the standard median absolute deviation statistic.

average absolute deviation about c = Σ|xᵢ−c|/n

c = mean or median

Variables and units

xáµ¢
each finite observation
c
selected center: mean or median
n
number of observations

Worked example

For 1,2,100 centered on the median 2, absolute distances are 1,0,98 and their average is 33.

Limitations

Mean, median, average deviation, total, and listed deviations are rounded to four decimals. Math.round retains the existing half-tie convention; if scaling for four-place rounding would overflow, the finite representable value is retained. Locale formatting is applied after numerical calculation.

  • Median-centered average absolute deviation must not be labeled as standard median absolute deviation (MAD).
  • Extremes still affect the average of deviations.
  • Derived values outside the supported finite numerical range are rejected with a localized input-field error.
  • All identical observations yield zero average absolute deviation.
  • For 1,2,100, standard median absolute deviation would be median(1,0,98)=1, not this mode’s 33.

Sources

Table of Contents

How to Use

  1. Enter your data values separated by commas, spaces, or semicolons
  2. Choose deviation type: from mean or from median
  3. Review the MAD, total absolute deviation, mean, and median

Calculate average absolute deviation from mean or median to measure data spread

Calculate average absolute deviation from the mean or from the median of a dataset. Method: Compute arithmetic mean and median, select one as the center, average absolute distances from that center, and also report their sum. Median-centered mode still averages distances; it does not compute the standard median absolute deviation statistic.

The Mean Absolute Deviation (MAD) provides a robust measure of variability that is less sensitive to extreme values compared to standard deviation.

Types of Absolute Deviation

There are two common types of absolute deviation:

  • Average distances from the selected mean or median center. A = Σ|xᵢ−center|/n; center ∈ {mean, median}.
  • The median-centered average is not the standard median absolute deviation statistic.

Interpreting Results

  • Lower MAD: Data points are closer to the center, indicating less variability
  • Higher MAD: Data points are more spread out, indicating greater variability
  • MAD of 0: All data points are identical
  • Total Absolute Deviation: Sum of all individual deviations, useful for understanding overall spread

Worked scenario

  • Three measurements: 1,2,100; center=2 → (1+0+98)/3=33.

MAD vs Standard Deviation

While both measure spread, they have key differences:

  • MAD uses absolute values; standard deviation uses squared differences
  • Extreme values contribute linearly to this average, unlike squared deviations in standard deviation; they still change the result.
  • Standard deviation is more commonly used in statistical inference
  • MAD is easier to interpret intuitively
  • Standard deviation has better mathematical properties for theoretical work

Method, example, rounding, and limits

Method: Compute arithmetic mean and median, select one as the center, average absolute distances from that center, and also report their sum. Median-centered mode still averages distances; it does not compute the standard median absolute deviation statistic.

Worked example: 1,2,100; center=2 → |−1|+0+98=99; A=33.

Rounding: 4 decimal places. Displayed values are rounded as stated beside the result.

Limit: Median-centered average absolute deviation must not be labeled as standard median absolute deviation (MAD). Combinations outside the supported numeric range are rejected.

Reference: NIST. https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm

Frequently Asked Questions

What's the difference between mean and median absolute deviation?
Average distances from the selected mean or median center. The median-centered average is not the standard median absolute deviation statistic.
When should I use MAD instead of standard deviation?
Use MAD when your data contains outliers or when you need a more intuitive measure of spread. MAD is less influenced by extreme values compared to standard deviation, which squares the differences.
Can absolute deviation be zero?
Yes, MAD equals zero only when all data points are identical (no variability). This indicates perfect consistency in the dataset.
How do I interpret a large MAD value?
A large MAD indicates high variability - data points are spread far from the center. In context, this could mean inconsistent measurements, high volatility, or diverse values depending on your application.

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