How to calculate the average (mean)
Updated on June 18, 2026 · by Rafael Rossi
The arithmetic mean is the most-used calculation in the world and one of the easiest to misread. Adding everything up and dividing by the count answers "what would each one get if the total were shared equally" — which is exactly the right question in some cases and exactly the wrong one in others.
The formula
Mean = (sum of all values) ÷ (number of values)
Example: scores of 7, 8 and 9. Sum = 24; count = 3; mean = 24 ÷ 3 = 8.
Weighted mean: when things count differently
In school and at work, almost nothing carries equal weight. In a weighted mean, each value is multiplied by its weight and the total is divided by the sum of the weights — not by the number of items.
Weighted mean = Σ(value × weight) ÷ Σ(weights)
A student scoring 6.0 (weight 2), 7.5 (weight 3) and 9.0 (weight 5):
| Score | Weight | Score × weight |
|---|---|---|
| 6.0 | 2 | 12.0 |
| 7.5 | 3 | 22.5 |
| 9.0 | 5 | 45.0 |
| Total | 79.5 | |
Mean = 79.5 ÷ 10 = 7.95. The unweighted mean of the same scores would be 7.50 — nearly half a point lower. The gap exists because the best score is the one that counts most.
The classic error is dividing by 3 (the number of tests) instead of by 10 (the sum of the weights). That gives 26.5, a meaningless number — and one that shows up regularly in hastily built spreadsheets.
What do I need on the final exam?
This is the most searched-for application of the mean, and it is a simple inversion:
Score needed = (target mean × number of tests) − sum of scores so far
With 5.0, 6.0 and 8.0 on the first three tests and a target mean of 7.0 across four: 7 × 4 = 28; 28 − 19 = 9.0. If the result exceeds the maximum on the scale, the target is mathematically out of reach — better to find that out before the exam than after.
When the mean lies
The mean is sensitive to extreme values, and a single outlier drags the whole thing. Consider eight salaries at a small company:
$40,000 · $44,000 · $48,000 · $50,000 · $56,000 · $60,000 · $64,000 · $500,000
The mean is $107,750. But seven of the eight people earn less than the mean — and the eighth is the owner. Saying "the average salary here is $107,750" is technically true and practically a lie.
The median — the middle value once everything is sorted — handles this case: here it is $53,000, which describes the typical experience far better. Rule of thumb: when a distribution has a long tail (income, house prices, waiting times), prefer the median.
The mean of percentages is not the percentage you got
An investment rises 100% one year and falls 50% the next. The arithmetic mean of those changes is +25% a year. The real result is zero: $100 becomes $200 and comes back to $100.
For chained growth rates the arithmetic mean is simply the wrong tool — the geometric mean is, and in that case it gives exactly 0%. The same applies to speed: driving out at 40 mph and back at 60 mph over the same route does not average 50 mph but 48 mph, because you spent more time at the slower speed.
Moving averages: the version that tracks time
When data swings hard day to day — sales, body weight, case counts — a single day's figure says nothing and the all-time mean hides the trend. The answer is a moving average: each day, take the mean of the last 7 days.
That strips out short-term noise (weekends, one odd day) and leaves the direction visible. It is why people tracking weight are told to watch the weekly average rather than today's scale: daily swings from water and gut content can reach 4 lb, far larger than any real change in body composition over 24 hours.
Frequently asked questions
Mean, median and mode — what is the difference? The mean is the total divided by the count; the median is the middle value of the sorted list; the mode is the value that appears most often. In a perfectly symmetric distribution all three coincide — and the further apart they drift, the more skewed the data.
How do I average grades with percentage weights? The same way: weights can be 20%, 30% and 50%, summing to 100 (or 1). Multiply each score by its weight and add them up — no division needed, because the weights already sum to 1.
Can I average a set of averages? Only if every group is the same size. The mean of a 10-student class average and a 40-student class average is not the school's average — for that you must weight each average by its number of students.
Do negative values break it? No, the calculation is unchanged. But be careful reading the result: a mean near zero can mean "all values are small" or "large values are cancelling each other out".