Add the numbers and divide by how many there are to get the mean; the median is the middle number once they are sorted, and the mode is the one that appears most often. Enter 2 to 12 numbers to see all four measures, with the range, at once.
The formula
Mean
mean = (x₁ + x₂ + … + xₙ) ÷ nMedian
the middle value when sorted, or the mean of the middle two if n is evenMode
the value that appears most often (none if every value appears once)Range
range = largest − smallestWorked example
Drop the 15s and use 3, 7, 9, 12 and 20: the mean is 10.2, the median is 9, there is no mode, and the range is 17.
When to use it, and the mistakes to avoid
Use it for marks across subjects, monthly figures, prices, survey answers, or any short list where you want one number that stands for the lot.
- Using the mean on skewed data. One extreme value drags it. Check the median as well.
- Forgetting to sort for the median. The middle of the list as typed is not the median.
- Averaging averages. The mean of two group averages is only right if the groups are the same size.
- Leaving a zero out. A zero is a value and lowers the mean. The calculator counts every box you have chosen to use.
- Expecting a mode in every list. If nothing repeats, there is none.
FAQ
What is the difference between mean, median and mode?
The mean is the sum divided by the count, the median is the middle value once the numbers are in order, and the mode is the value that appears most often. For 12, 15, 15, 18, 22 and 30 they are 18.67, 16.5 and 15.
When is the median better than the mean?
When a few very large or very small values would pull the mean away from what is typical. Incomes and house prices are the classic cases: one billionaire in a village raises the mean income a great deal and leaves the median where it was.
Can a set of numbers have more than one mode?
Yes. If two or more values tie for the most appearances, every one of them is a mode, and the calculator lists them all. 2.5, 2.5, 7 and 7 has the two modes 2.5 and 7.
What if no number repeats?
Then there is no mode. A list in which every value appears once has nothing that appears 'most often', so the calculator says so instead of listing every number.
How do I find the median of an even number of values?
Sort the numbers and take the mean of the two in the middle. For 1, 2, 3 and 4 the middle two are 2 and 3, so the median is 2.5. The calculator sorts the list for you, so you can enter the numbers in any order.