How this calculator works
Enter any list of numbers, separated by commas, spaces, or new lines, and this calculator returns every common summary statistic at once: the mean (arithmetic average), median (middle value), mode (most frequent value), range, minimum, maximum, sum, and count. It's built for quickly checking a data set without opening a spreadsheet.
Mean, median, and mode all try to answer "what's typical here", but they can disagree, especially with skewed data or outliers. Looking at all three together, along with the range, gives a fuller picture than any single number.
The formulas
Mean: sum of all values ÷ count of valuesMedian: the middle value when sorted (odd count), or the average of the two middle values (even count)Mode: the value or values that occur most often; if every value is unique, there is no modeRange: maximum − minimumWorked example: 2, 4, 4, 4, 5, 5, 7, 9
- Sum: 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40. Count: 8. Mean = 40 ÷ 8 = 5.
- Sorted, the two middle values (4th and 5th) are 4 and 5, so the median = (4 + 5) ÷ 2 = 4.5.
- 4 appears three times, more than any other value, so the mode is 4.
- Range = maximum (9) − minimum (2) = 7.
Frequently asked questions
What's the difference between mean, median, and mode?
The mean is the arithmetic average of every value. The median is the middle value once the data is sorted, which resists being skewed by a few extreme outliers. The mode is simply the value that shows up most often, and a data set can have one mode, several tied modes, or no mode at all.
How is the median calculated when there's an even number of values?
Sort the list, then average the two values sitting in the middle. For 1, 2, 3, 4 the middle pair is 2 and 3, so the median is 2.5.
What if two or more values are tied for most frequent?
The set is multi-modal — all of the tied values are reported as the mode. For 1, 1, 2, 2, 3 both 1 and 2 appear twice, so the mode is "1, 2".
Why is the mean sometimes very different from the median?
The mean is pulled toward extreme values (outliers), while the median is not. Household income data is a classic example: a handful of very high incomes raise the mean well above the median, which better reflects the typical household.
Can the average of a data set be a number that isn't in the list at all?
Yes — the mean and median often aren't any of the original values. For the set 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5 (which happens to appear in the list) but the median is 4.5, a value that isn't in the data set at all, since it's the average of the two middle values 4 and 5.