Weighted Averages
Averaging numbers that represent different-sized groups by weighting each by its size, so a big segment counts more than a small one.
What it is
A weighted average is what you compute when the numbers you are averaging represent groups of different sizes and you want each to count in proportion to its importance. A plain average treats every value equally; a weighted average lets a larger group pull the result toward its value. This is the correct way to combine segment margins, regional prices, product mixes, or any set of rates that sit on top of different volumes. The core idea is that you cannot average rates or ratios by simply averaging the rates - you have to reweight by the underlying quantities, or you get an answer that is quietly, sometimes badly, wrong.
When to use it
Use it whenever you are combining rates, prices, margins, or percentages that apply to groups of unequal size - blended margin across products, average price across regions, overall conversion rate across channels, portfolio return across holdings. It is the honest way to roll segment-level figures up to a company-level number. It is unnecessary when the groups are genuinely equal in size, where a plain average and a weighted average coincide. Do not average percentages naively when they sit on different bases; that is the single most common quantitative error in case interviews.
How to apply it
The formula is: Weighted average = sum of (each value x its weight) / sum of the weights. The weights are the group sizes - units, customers, revenue, whatever the values sit on top of. Keep the unit discipline: if you are averaging margin percentages, weight by the volume or revenue each margin applies to, not by nothing. A quick mental check: the weighted average must land between the smallest and largest values, and closer to the value of the biggest group. Interpretation: the result is the single figure that, applied to the whole, reproduces the true total - so a blended margin times total revenue should equal total contribution. If it does not, the weighting is wrong.
Common mistakes
The dominant error is averaging percentages or rates directly - taking a 40% margin and a 10% margin and calling the blend 25% - when the two products sell in wildly different volumes. If 90% of units are the low-margin product, the true blended margin is near 10%, not 25%. Another mistake is weighting by the wrong quantity (units when you should weight by revenue, or vice versa). People also forget the sanity check that the answer must fall between the extremes and lean toward the larger group, so they miss obviously impossible results.
Example
A software company reports two products: an enterprise tier at 80% gross margin and a consumer tier at 30% gross margin, and someone states the 'average margin is 55%'. But the consumer tier is 85% of revenue and enterprise only 15%. The true blended margin weights by revenue: 0.15 x 80% + 0.85 x 30% = 12% + 25.5% = 37.5%, far below the naive 55%. That 17-point gap completely changes the profitability picture and any decision resting on it. The weighted-average discipline - and the sanity check that the blend must sit near the big segment's 30% - catches an error that would otherwise cascade through the whole analysis.
Practice it
Practice on profitability, pricing, and mix cases by always weighting rates by their underlying volume or revenue, never averaging percentages directly, and checking that the blend lands between the extremes and near the largest group. The skill to build is the reflex to ask 'what does each of these percentages sit on top of?' before combining them.