Mean, median and mode calculator
Paste or type your numbers, separated by commas, spaces or new lines, and get every common average plus the spread of the data.
How the mean, median and mode calculator works
The mean adds everything up and divides by how many values there are. The median is the middle value once the list is sorted. The mode is the value that appears most often. The range is the gap between the largest and smallest values, and it gives a quick feel for how spread out the data is.
The standard deviation measures typical distance from the mean. Use the population version if your list is every value that exists, and the sample version if it is only a sample of something bigger.
The formula behind it
- Mean = sum of values ÷ number of values
- Median = middle value (or the average of the middle two)
- Range = largest - smallest
A worked example
For 4, 8, 6, 8, 10, 12: the total is 48 and there are 6 values, so the mean is 8. Sorted, the list is 4, 6, 8, 8, 10, 12; the middle two are both 8, so the median is 8. The number 8 appears twice, so the mode is 8, and the range is 12 - 4 = 8.
Questions people ask
Which average should I use?
The mean uses every value but is pulled around by extremes. The median ignores extremes, which is why house prices are usually reported as medians. The mode suits categories, like the most common shoe size.
Can there be more than one mode?
Yes. If two values tie for most frequent, the data is bimodal and both are listed. If nothing repeats, there is no mode.
What is the difference between sample and population?
The sample version divides by n - 1 to correct for the fact that a sample tends to underestimate the true spread.
Why is my median not in my list?
With an even number of values the median is halfway between the two middle ones, which may not be a value you typed.