Weighted average

A weighted average is an arithmetic mean where each value is multiplied by a weight before summing, and the sum is divided by the total weight rather than the count. Formula:

weighted_mean = Σ(wᵢ × xᵢ) / Σ(wᵢ)

If all weights are equal, the weighted average reduces to the regular mean. If one value has weight zero, it doesn’t affect the result.

Where weighted averages appear:

• GPA (US grade-point average). Course grades weighted by credit hours. A 4-credit A counts more than a 1-credit A.
• Blended interest rates. Borrower with $200k at 6% and $50k at 4% has a weighted rate of (200×6 + 50×4) ÷ 250 = 5.6%.
• Polling and surveys. Demographic groups are weighted to match the population, so an undersampled group counts more per respondent.
• Index funds. Market-cap-weighted indices (S&P 500) weight constituents by their market cap. Equal-weighted variants assign equal weight regardless.
• Moving averages in time series. Exponentially-weighted moving averages weight recent data more heavily than old data.

Common mistakes: using counts where weights are required (averaging percentages without weighting by sample size produces “Simpson’s paradox” results), or weighting by the wrong dimension entirely. When the question is “what’s the average X across the population,” the right weights are the population frequencies, not raw counts of observations.