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Math"The average salary here is $90,000" — but nobody you know earns that. Welcome to the most misused statistic in everyday life. There are three different averages, each answering "what's typical?" in its own way, and choosing the wrong one is how data lies while telling the truth.
This guide defines mean, median, and mode, shows when each wins, and covers weighted averages — the version hiding inside your GPA.
Try it yourself: Compute mean, median, and mode for any dataset. Mean / Median / Mode Calculator →
The three definitions
Mean = sum of values ÷ count
Median = middle value of sorted data
Mode = most frequent value
Median = middle value of sorted data
Mode = most frequent value
Test scores of 70, 80, 80, 90, 100: the mean is 420 ÷ 5 = 84; the median (middle of sorted list) is 80; the mode is 80 (appears twice). For nicely behaved data, all three agree — the interesting cases are when they don't.
When the mean lies: the billionaire example
Nine coworkers earn $50k each; the CEO earns $5M. The mean salary is ($450k + $5M) ÷ 10 = $545k — a number nobody in the building earns. The median is $50k — what a typical employee actually takes home.
This is why housing prices, incomes, and company revenues are almost always reported as medians: real-world distributions are skewed, and the mean gets dragged toward the extreme tail. The mean isn't wrong — it's just answering a different question ("what's the total divided evenly?"), which is rarely the question being asked.
When each average wins
| Situation | Best average | Why |
|---|---|---|
| House prices in a city | Median | Luxury outliers skew the mean |
| Average test score for grading | Mean | Every point counts equally |
| Most popular shoe size | Mode | You want the peak of demand, not the center |
| Typical commute time | Median | A few disaster days distort the mean |
| Survey: favorite color | Mode | Categories have no mean or median |
Note the last row: the mode is the only average that works on categorical data. "Average favorite color" is meaningless, but the mode is blue (or whatever wins the survey).
Weighted averages: when some values count more
A course grade with a 40% final, 30% midterm, and 30% homework is a weighted average:
Weighted average = Σ(value × weight) ÷ Σ(weights)
Final 88, midterm 76, homework 94: (88×0.4) + (76×0.3) + (94×0.3) = 35.2 + 22.8 + 28.2 = 86.2. A plain mean (86) would underweight the final. GPAs work the same way — credits are the weights, which is why an A in a 4-credit course moves your GPA more than an A in a 1-credit course.
The average of averages trap
Two classes average 80 and 90. The school average is not 85 — unless the classes are the same size. If class A has 30 students and class B has 10, the true average is (30×80 + 10×90) ÷ 40 = 82.5. Averaging averages without weighting by group size is one of the most common real-world statistics errors — always weight by the underlying counts.
Frequently asked questions
The mean is the sum divided by the count — the arithmetic average. The median is the middle value when data is sorted. The mode is the most frequent value. Each describes "typical" differently and each can mislead in different situations.
When data is skewed by outliers. Income, house prices, and waiting times are classic cases — a few extreme values drag the mean far from what most people experience, while the median stays representative.
Yes. Data with two equally frequent peaks is bimodal, and with several peaks, multimodal. A dataset where every value appears once has no mode at all. The mode is most useful for categorical data like colors, brands, or survey answers.
An average where some values count more than others. Multiply each value by its weight, sum the results, and divide by the total weight. GPAs, course grades, and investment returns all use weighted averages.
Disclaimer: Calculator content is for education only — examples are illustrative and rounded; double-check figures used in financial or contractual decisions.