The difference is what gets counted equally
A simple average adds values and divides by the number of values. For test scores of 70, 80, and 90, the simple average is 80. Each score contributes equally. That makes sense when each score represents one comparable observation and the question is, “What is the average score?”
A weighted average is useful when the values represent different numbers of observations or have different, justified levels of importance. Instead of treating every value equally, you multiply each value by its weight, add those products, and divide by the sum of the weights. The calculation is straightforward; deciding what the weights should represent takes more thought.
Why averaging group averages can go wrong
Imagine two classes took the same test. A class of 10 students had an average score of 90, while a class of 30 students had an average of 70. Averaging the two class averages gives 80. But 80 is not the average score across all 40 students: it gives the smaller class the same influence as the class with three times as many students.
To find the combined student average, use class sizes as weights. The first class accounts for 10 × 90 = 900 points; the second accounts for 30 × 70 = 2,100 points. Together, that is 3,000 points across 40 students, so the combined average is 75. The simple average of 80 answers a different question: what is the average of the two class averages? Neither calculation is inherently wrong, but only one describes the average student score.
How to calculate a weighted average
Start by listing each value beside its weight. Multiply each pair, add the results, then divide by the total weight. For example, suppose a course grade consists of assignments worth 40% and an exam worth 60%. If a student scores 85 on the assignments and 70 on the exam, the weighted result is (85 × 0.40) + (70 × 0.60) = 76. Because the weights add to 1, there is no further division needed.
Weights need not be percentages. In the class example, 10 and 30 are weights, and their sum is 40. Percentages simply express those same shares as 25% and 75%. Before calculating, check that the weights match the question. Class size is appropriate for an average across students; a course grading policy calls for the stated grade weights. Choosing convenient weights rather than meaningful ones can make a precise-looking answer misleading.
Rates need careful denominators
Averages of percentages can be especially deceptive when the underlying groups differ in size. Suppose one team completes 2 of 10 requests, a 20% completion rate, and another completes 80 of 100, an 80% rate. The simple average of the two rates is 50%. Across all requests, however, 82 of 110 were completed, giving a combined rate of about 74.5%.
If the question concerns a randomly selected request from the combined set, total the completed requests and total requests first. If the question concerns a typical team’s rate, the simple average of team rates may be relevant instead. Always note what sits beneath each percentage: requests, people, hours, or something else. A rate cannot be combined meaningfully without a clear definition of both its numerator and its denominator.
An average still cannot show the whole distribution
Even a correctly weighted average can conceal important variation. Two groups might have the same average score while one has scores clustered near that number and the other has scores spread widely. A few unusually large or small values can also pull an average away from what most observations look like. When that distinction matters, report the group sizes and consider showing the range, median, or separate group results alongside the average.
Before publishing an average, ask three questions: What is being averaged? What does each value represent? What decision will a reader make from the result? If each value is one comparable observation, a simple average may be enough. If values summarize differently sized groups, a weighted average is often needed. Showing the weights and the question they answer makes either result easier to interpret—and harder to misuse.
