Average Calculator: Mean, Median, Mode
Mean, median, mode and range for any list of numbers.
Good to know. When a billionaire walks into a room, the average income soars and the median doesn’t move.
How it works
In plain words
The mean is the sum divided by how many numbers there are. The median is the middle number once they’re sorted (or the average of the two middle numbers). The mode is the number that appears most often.
The formula
mean = (x₁ + x₂ + … + xₙ) ÷ n median = middle value of the sorted list range = largest − smallest
Worked example
4 + 8 + 15 + 16 + 23 + 42 = 108, and 108 ÷ 6 = 18. The median is (15 + 16) ÷ 2 = 15.5.
Sources
No outside data or rates: this is plain arithmetic.
8 automated tests check its answers on every change.
About the average calculator: mean, median, mode
When people say "average", they usually mean the mean: add everything up and divide by how many there are. It is the right choice for most everyday questions, like the average of your test scores, your monthly spending or your running times.
The mean has one weakness: it is pulled around by extreme values. If nine people earn 30,000 and one earns 3,000,000, the mean income is 327,000, which describes nobody. That is where the median helps. It is the middle value once the numbers are sorted, so a few very large or small values don’t move it much. House prices and incomes are usually reported as medians for this reason.
The mode is the value that appears most often. It is most useful for things that repeat, like shoe sizes sold or the most common answer in a survey. A list can have more than one mode, or none at all if every value is different.
The range, the gap between the smallest and largest value, gives a quick sense of how spread out the numbers are.
To use the calculator, paste or type your numbers separated by commas, spaces or line breaks. You can copy a column straight from a spreadsheet.
Questions people ask
How do I calculate the average?
Add all the numbers and divide by how many there are. 4, 8, 15, 16, 23 and 42 add up to 108, and 108 ÷ 6 = 18.
What is the difference between mean and median?
The mean is the sum divided by the count. The median is the middle value when sorted. The median is less affected by extreme values.
How do I find the median of an even number of values?
Sort them and take the average of the two middle values. For 4, 8, 15, 16, 23, 42 that is (15 + 16) ÷ 2 = 15.5.
Can there be more than one mode?
Yes. If two or more values tie for most common, they are all modes. If every value appears once, there is no mode.