Average Calculator (Mean, Median, Mode)
mean 95
How do you find the average?
The average of a list is one number that stands for the whole list, and three different figures answer to that name: the mean, the median and the mode.
- Paste your numbers into the box above, separated by commas, spaces or line breaks. The mean is the sum of the values divided by how many values there are.
- Sort the list from smallest to largest and read the middle of it. The median is the middle value once the list is sorted; with an even count it is the mean of the two middle values.
- Count how often each value appears. The mode is the value that occurs most often, and a list can have more than one mode or none at all.
- Take the smallest value away from the largest. The range is the largest value minus the smallest, and it describes the spread rather than the centre.
- Read the three figures side by side before you quote one. Mean, median and mode are three different answers to "what is typical here": for 85, 100 and 100 they are 95, 100 and 100.
Every figure this page works out, for one list
The widget fills these same six rows for whatever you paste in. The row below each label says what that figure answers, so you can tell at a glance which one your question wants.
| Statistic | What it answers | For 85, 100, 100 |
|---|---|---|
| mean | the middle of the total | 95 |
| median | the middle of the sorted list | 100 |
| mode | the value that turns up most | 100 |
| range | how far apart the ends are | 15 |
| sum | everything added together | 285 |
| count | how many values there are | 3 |
Worked Example: 85, 100 and 100
95 is the mean. 85, 100, 100: mean 95, median 100, mode 100, range 15, sum 285, count 3.
85, 100, 100 → mean 95, median 100, mode 100
The mean is the only one of the three that moved. It sits below both hundreds because 85 pulls it down, while the median and the mode stay where the repeated value is. That gap is the whole reason to look at more than one figure.
Which Average Should You Use?
When the mean is the figure you want
Use the mean when every value counts the same and none of them is far out of line with the rest. It uses all of your data, which is its strength and also its weakness: one value ten times the size of the others moves it a long way.
When the median is the figure you want
Use the median when a few values sit far from the rest — house prices, salaries, response times. It reports the middle of the sorted list, so an outlier changes which value sits in the middle but not by how much.
When the mode is the figure you want
Use the mode when the values are labels rather than quantities, such as shirt sizes or star ratings. It is the only one of the three that still means something when the numbers cannot be added.
What this page averages
It averages a list of numbers. Fuel consumption over a tank, a batting average and an average of times all have their own rules about what goes into the list, and this page does not apply them for you.
Frequently Asked Questions
What is the difference between the mean, the median and the mode?
They answer the same question in three ways. The mean uses every value, the median uses only the middle of the sorted list, and the mode uses how often each value appears.
How do you calculate an average percentage?
Total the parts, total the group sizes, and divide once. Averaging percentages works only when each one covers the same size group: 40 out of 50 and 10 out of 200 is 20 percent overall, not the 42.5 percent a plain mean of 80 and 5 would give.
What is a weighted average?
A weighted average multiplies each value by how much it counts, adds those products, then divides by the total of the weights. Use it when some values count for more than others.
How do you work out a class average?
Paste the marks into the box above and read the mean. Where some pieces of work count for more than others, switch the control to weighted values and give each mark its weight.
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