Average Calculator
Mean, median, mode, range and sum from any list of numbers.
About this calculator
Paste numbers โ separated by spaces, commas or new lines โ and read the whole statistical family at once: mean, median, mode, count, sum and range, with the working for the mean and median written out underneath.
Which average to trust
The three averages answer different questions, and choosing the wrong one is how statistics mislead. The mean (sum รท count) uses every value, which is its strength and its weakness: one outlier drags it โ a single billionaire in a bar raises the mean income by millions while everyone's pockets stay the same. The median (middle of the sorted list) ignores magnitude beyond order, which is why house prices and incomes are reported as medians. The mode (most frequent) is the only average that works for categories โ shoe sizes, survey answers โ and the honest answer to "what's typical?". The practical rule: mean for well-behaved data, median when outliers or skew are suspected, mode for counts of kinds. When the mean and median disagree badly, that disagreement is itself the finding. For how spread out the data is, standard deviation picks up where range leaves off.
Frequently asked questions
What's the difference between mean and median?
Mean is sum รท count; median is the middle of the sorted list. They agree on symmetric data and split when outliers or skew appear โ the median resists extremes, which is why incomes and house prices use it.
When is the mode useful?
For categories and repeats โ the most common shoe size, survey answer or test score. It's the only average that makes sense for non-numeric data.
How is the median found with an even count?
Average the two middle values of the sorted list: for 4, 8, 10, 20 the median is (8 + 10) รท 2 = 9. The calculator notes when it's done this.
Why do mean and median disagree?
Skew. A long tail of large values pulls the mean toward it while the median stays with the crowd โ the gap between them is a quick measure of how skewed the data is.