The three averages
mean = sum ÷ count · median = middle sorted value · mode = most frequent value
"Average" usually means the mean: add everything up and divide by how many numbers there are. But the median and mode are averages too, and each answers a different question — the mean is the balancing point, the median is the typical middle case, and the mode is the most common value.
Worked example
For the default list 12, 15, 11, 18, 15, 9: the sum is 80 and there are 6 numbers, so the mean is 80 ÷ 6 ≈ 13.33. Sorted, the list is 9, 11, 12, 15, 15, 18; with an even count the median is the mean of the two middle values, (12 + 15) ÷ 2 = 13.5. The value 15 appears twice, more than any other, so the mode is 15. The range is 18 − 9 = 9.
Which one should I use?
Use the mean when values are roughly symmetric — test scores, temperatures, batch weights. Use the median when a few extreme values would distort the picture — salaries, house prices, wait times. Use the mode for categorical or "most popular" questions — shoe sizes, poll answers, dice results. If all values are distinct there simply is no mode.
Range, min and max
The range (maximum − minimum) is the crudest measure of spread: it tells you how far apart the extremes are, but nothing about what happens in between. If you need a proper measure of spread, pair this page with the standard deviation calculator.