“The average” is ambiguous. A handful of very large or very small values can pull one kind of average a long way while leaving another untouched. Knowing all three tells you more than any one alone.
The three measures
- Mean: add everything up and divide by how many numbers there are.
- Median: sort the numbers and take the middle one, or the mean of the two middle ones if there is an even count.
- Mode: the value that appears most often. A list can have no mode, one, or several.
The range is the largest value minus the smallest, a quick measure of spread.
A worked example
Take 4, 8, 6, 5, 3, 8, 9. The sum is 43 across 7 values, so the mean is 6.14. Sorted, the list is 3, 4, 5, 6, 8, 8, 9, and the middle value is 6. The number 8 appears twice, so the mode is 8. The range is 9 − 3 = 6.
With an even count, such as 3, 5, 5, 7, 7, 9, the median is the mean of the two middle values, 5 and 7, which is 6. Here 5 and 7 each appear twice, so the calculator reports two modes: 5 and 7.
Using the calculator
- Open the Average Calculator and paste your numbers, separated by commas, spaces or new lines.
- Read the mean, median, mode, range and count.
Which one to use
Use the median when a few extreme values would distort the mean, which is why household income is usually reported as a median. Use the mean when values are fairly even and you want every number to count. Use the mode for categories or common sizes, such as the shoe size most often sold. If mean and median differ a lot, that gap itself tells you the data is skewed.
Frequently asked questions
What if every number appears only once?
Then there is no mode. A list where several values tie for most frequent has more than one.
Does the order I type the numbers matter?
No. The calculator sorts them for the median and counts them for the mode, so any order gives the same answer.
How is this different from standard deviation?
Averages describe the centre, while standard deviation describes how spread out the numbers are around it. See the standard deviation guide.