Mean, median and mode calculator
Paste or type a list of numbers to get the mean, median, mode, range, quartiles, variance and standard deviation. The sorted list and the working are shown.
Worked example
With the values shown above when the page opens:
Mean 6.222222, median 6, mode 8
- Sorted: 3, 4, 5, 5, 6, 8, 8, 8, 9
- Mean = sum ÷ count = 56 ÷ 9 = 6.222222
- Median = the middle value (position 5) = 6
- Mode = the most frequent value
- Variance = the average squared distance from the mean; standard deviation is its square root
How it works
- The mean is the sum divided by how many numbers there are.
- The median is the middle number when the list is sorted (or the average of the two middle numbers).
- The mode is the number that appears most often. A list can have more than one mode, or none.
- The range is the largest number minus the smallest. Standard deviation measures how spread out the numbers are.
- Quartiles use the median of the lower half and the upper half, leaving out the middle value when there is an odd number of values.
Questions
What is the difference between population and sample standard deviation?
Use population when your list is every value you care about. Use sample when it is a sample from a larger group; it divides by n − 1 instead of n.
Which is better, mean or median?
The median is less affected by extreme values. For incomes or house prices it often describes a typical case better than the mean.
Can there be no mode?
Yes, if no value repeats. This calculator then says no value repeats.
Related
Calculators are for learning and quick checks. Check important figures yourself, and do not rely on them for tax, legal or financial decisions.