OneTaskBy Tim King · Updated
Average Calculator
Mean, Median, Mode and Range of a List of Numbers
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How the Average Calculator works
This average calculator finds the mean, median, mode and range of any list of numbers. Paste values separated by commas, spaces or new lines, straight from a spreadsheet column if you like. You also get the count, sum, minimum and maximum, the sorted list, and for positive data the geometric and harmonic means.
"Average" can mean three different things, and they tell different stories. The mean shares the total out equally, the median is the middle value, and the mode is the most common one. With salaries or house prices a few very large values drag the mean up, so the median is often the fairer typical figure. The range shows how spread out the data is, from the smallest to the largest value.
How the average calculator works
The formula for the mean is the sum of the values divided by how many there are. The median is the middle value after sorting, or the mean of the two middle values when the count is even. The mode is the value that appears most often; there can be several, or none if every value is unique. The range is the maximum minus the minimum.
First example. For 3, 5, 5, 7, 7, 9 the sum is 36 over 6 values, so the mean is 6. The middle pair is 5 and 7, so the median is 6, and 5 and 7 are both modes.
Second example. For 1, 2, 3, 4, 100 the mean is 22 but the median is 3, showing how one outlier pulls the mean.
How many values do I need for a median? Any number; with an odd count it is the single middle value.
Mean, median and mode side by side for small data sets
| Data | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 2, 4, 6, 8, 10 | 6 | 6 | None | 8 |
| 1, 2, 3, 4, 100 | 22 | 3 | None | 99 |
| 3, 3, 4, 5, 10 | 5 | 4 | 3 | 7 |
| 7, 7, 7, 7 | 7 | 7 | 7 | 0 |
| 1, 2, 3, 4 | 2.5 | 2.5 | None | 3 |
| 10, 20, 30, 40, 50, 60 | 35 | 35 | None | 50 |
| 5, 1, 4, 1, 5, 9, 2, 6 | 4.125 | 4.5 | 1, 5 | 8 |
| 1, 1, 2, 3, 5, 8, 13 | 4.714286 | 3 | 1 | 12 |
| 12, 15, 15, 18, 20 | 16 | 15 | 15 | 8 |
| 0, 0, 0, 100 | 25 | 0 | 0 | 100 |
| 40, 45, 50, 55, 200 | 78 | 50 | None | 160 |
| 2, 8 | 5 | 5 | None | 6 |
| 1, 10, 100 | 37 | 10 | None | 99 |
| 60, 70, 80, 90, 100 | 80 | 80 | None | 40 |
| 3, 5, 5, 7, 7, 9 | 6 | 6 | 5, 7 | 6 |
| -5, 0, 5 | 0 | 0 | None | 10 |
| -10, -2, 4, 8 | 0 | 1 | None | 18 |
| 1.5, 2.5, 3.5 | 2.5 | 2.5 | None | 2 |
| 100, 101, 102, 1000 | 325.75 | 101.5 | None | 900 |
| 9, 9, 9, 1 | 7 | 9 | 9 | 8 |
| 25, 30, 35, 40, 45, 50, 1000 | 175 | 40 | None | 975 |
| 6, 6, 6, 6, 6, 60 | 15 | 6 | 6 | 54 |
Tips and pitfalls
- Outliers skew the mean. Use the median for incomes, prices and waiting times.
- Sort before finding the median. The middle of an unsorted list means nothing.
- Weighted marks need weights. If tests count differently, use a weighted average instead.
- Use the geometric mean for growth. Average returns of +50% and -50% are not 0% overall.
FAQ
How do you calculate the average?
Add all the numbers and divide by how many there are. For 4, 8 and 15 the sum is 27 and there are 3 numbers, so the average is 9. This is the arithmetic mean, which is what most people mean when they say average.
What is the difference between mean, median and mode?
The mean is the total divided by the count, the median is the middle value when sorted and the mode is the most frequent value. For 1, 2, 2, 3, 12 they are 4, 2 and 2. When they are close together the data is roughly symmetric; when far apart it is skewed.
How do you find the median of an even number of values?
Sort the values and take the mean of the two in the middle. For 3, 7, 8, 12 the middle pair is 7 and 8, so the median is 7.5. With an odd count there is a single middle value, so no averaging is needed.
Can there be more than one mode?
Yes. A data set with two values tied for most frequent is bimodal, such as 2, 2, 5, 5, 9, where 2 and 5 are both modes. If every value appears exactly once there is no mode at all, and the calculator says so.
When should I use the geometric mean?
Use it for rates that multiply, such as growth or investment returns. Growth of 10% then 50% gives a geometric mean of √(1.1 × 1.5) ≈ 1.2845, about 28.5% a year, which reproduces the real total. The plain mean of 30% would overstate it.
See also: all Statistics tools, Arithmetic, Number Theory, Algebra and Geometry, Trigonometry and Calculus.
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