LaTeX
\bar x_w=\frac{\sum_i w_ix_i}{\sum_i w_i}Variables
- wᵢ: weights
- xᵢ: values
How to use this formula
Calculates an average where observations have different weights.
Important notes
- Weights should be nonnegative for most applications.
Quick example
Values 10,20 with weights 1,3 give 17.5.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Weights should be nonnegative for most applications.
- For the Weighted Mean, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Weighted Mean, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- For the Weighted Mean, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
Values 10,20 with weights 1,3 give 17.5.
Common mistakes
- When copying Weighted Mean, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Weighted Mean, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Weighted Mean 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
\bar x_w=\frac{\sum_i w_ix_i}{\sum_i w_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 Weighted Mean used for?
Calculates an average where observations have different weights.
Can I copy this formula as LaTeX?
Yes. Copy \bar x_w=\frac{\sum_i w_ix_i}{\sum_i w_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.