LaTeX
MAE=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat y_i|Variables
- y_i: observed value
- ŷ_i: prediction
- n: count
How to use this formula
Averages absolute prediction errors.
Important notes
- MAE is less sensitive to extreme errors than MSE.
- It remains in the original response units.
Quick example
Absolute errors 1,1,2 give MAE=4/3.
Applicability, worked calculation, and verification
Assumptions and domain checks
- MAE is less sensitive to extreme errors than MSE.
- For the Mean Absolute Error, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Mean Absolute Error, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- For the Mean Absolute Error, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
Absolute errors 1,1,2 give MAE=4/3.
Common mistakes
- When copying Mean Absolute Error, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Mean Absolute Error, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Mean Absolute Error in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
MAE=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat y_i|. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Mean Absolute Error used for?
Averages absolute prediction errors.
Can I copy this formula as LaTeX?
Yes. Copy MAE=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat y_i| or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.