How to use the calculator
- Enter your numbers, separated by commas, spaces or new lines. Decimals and negative numbers are fine.
- Read the four answers. The mean is the large number; the median, mode and range are underneath.
- Follow the step-by-step list to check your own working, and the frequency table to see how often each value appears.
What each one means
The mean, median and mode are three ways to describe the center of a list, often called "averages". The range is different: it measures the spread, how far apart the extremes are. Always sort the list before finding the median, or you will pick the wrong middle value.
Worked example
The calculator starts with these ten quiz scores: 8, 3, 5, 12, 5, 9, 7, 5, 10, 6.
- Sort them: 3, 5, 5, 5, 6, 7, 8, 9, 10, 12
- Mean: the total is 70, and there are 10 values, so 70 ÷ 10 = 7
- Median: 10 is an even count, so take the 5th and 6th values, 6 and 7, and find the halfway point: (6 + 7) ÷ 2 = 6.5
- Mode: 5 appears three times, more than any other score, so the mode is 5
- Range: 12 − 3 = 9
Here the mean (7), median (6.5) and mode (5) are all different. That is normal: they measure the center in different ways.
Odd and even counts
With an odd number of values, the median is the one in the exact middle. For 4, 1, 9, sorted as 1, 4, 9, the median is 4: there is one value on each side of it. The mean is 14 ÷ 3 = 4.66667.
With an even number of values, there is no single middle, so you average the two in the center. A quick way to find the position: for n sorted values, the median sits at position (n + 1) ÷ 2. For 10 values that is position 5.5, halfway between the 5th and 6th.
Special cases for the mode
| List | Mode |
|---|---|
| 2, 4, 4, 7 | 4 |
| 1, 2, 2, 3, 3 | 2 and 3 (two modes, "bimodal") |
| 3, 6, 8, 11 | No mode: nothing repeats |
| 5, 5, 9, 9 | No mode: every value appears equally often |
The mode is the only one of the four that works for non-number data too, such as the most common shoe size or favorite color.
Frequently asked questions
Which average should I use?
Use the mean when the values are fairly even, such as test scores in a class. Use the median when a few values are much bigger or smaller than the rest, such as house prices, because one mansion can pull the mean up a lot. Use the mode for the most common choice or size. The statistics calculator also shows quartiles and outliers if you need more.
Can the mean be a number that isn't in the list?
Yes. The mean of 1, 2, 2, 3 and 3 is 11 ÷ 5 = 2.2, which none of the values equals. The median of an even-sized list can also fall between two values, like the 6.5 in the example.
Can a list have more than one mode?
Yes. If two or more values tie for appearing most often, each one is a mode. If every value appears the same number of times, the list has no mode at all.
Does the range tell me if the data is spread out?
It gives a quick idea, but one extreme value can make it large even when most values are close together. The standard deviation measures spread using every value; try the standard deviation calculator.
Related calculators
- Statistics Calculator — Descriptive statistics for a list: mean, median, mode, quartiles, IQR, outliers, variance, SD and skewness.
- Standard Deviation Calculator — Sample and population standard deviation, variance and mean of a list of numbers, with every step shown.
- Average Calculator — The mean of a list of numbers with the working shown, plus a weighted average for grades and scores.
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