Calculators
Weighted Mean Absolute Deviation Calculator
Calculate weighted mean absolute deviation about the weighted arithmetic mean from values and relative weights privately in your browser.
Measure absolute spread with relative weights.
Weighted mean absolute deviation averages absolute distances from the weighted arithmetic mean: μ = Σ(w × x) / Σw and deviation = Σ(w × |x − μ|) / Σw. For values 2, 4, and 7 with weights 1, 2, and 1, the weighted mean is 4.25 and the weighted mean absolute deviation is 1.375. Weights represent relative importance or frequency; multiplying all weights by a common positive factor leaves the result unchanged. Zero-weight rows are ignored. A single positive-weight observation or identical active values gives zero deviation. This is distinct from median absolute deviation and weighted standard deviation, which uses squared distances. Enter up to 10000 pairs, one per line, separating each value and weight with a comma, semicolon, or spaces. Values may be signed; weights must be non-negative with at least one positive. Nonzero magnitudes must be between 1e-100 and 1e100. Scientific notation is supported; omit thousands separators. Use consistent units; the result shares those units. Scaled values, normalized weights, and compensated summation reduce overflow and rounding error. Browser floating-point limits can still discard tiny relative contributions; results show up to 12 significant digits. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is weighted mean absolute deviation calculated?
First calculate μ = Σ(w × x) / Σw, then calculate Σ(w × |x − μ|) / Σw. For 2, 4, and 7 with weights 1, 2, and 1, μ is 4.25 and the deviation is 1.375.
Do weights need to sum to one?
No. Any non-negative relative weights are accepted, provided at least one is positive. Scaling every weight by the same positive factor leaves the result unchanged. Zero-weight rows are ignored.
Is this weighted standard deviation or median absolute deviation?
No. This tool averages absolute distances from the weighted arithmetic mean. Standard deviation uses squared distances and a square root; median absolute deviation uses medians.
Which inputs are supported?
Enter up to 10000 value and weight pairs, one per line. Signed values and zero are accepted; weights must be non-negative. Nonzero magnitudes must be between 1e-100 and 1e100. Scientific notation is supported.
What units does the result use?
The mean and absolute deviation have the same units as the values. Identical positive-weight values or one positive-weight observation have zero deviation. Processing stays in your browser; floating-point rounding affects extreme ratios.