Average calculator
Mean, median, mode and range, with the working
Type or paste your numbers, separated by commas, spaces or new lines.
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- Median (middle)
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- Mode (most common)
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- Range (largest − smallest)
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- Count and total
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- In order
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Working, step by step
Four kinds of average
"Average" usually means the mean, but the median and mode are averages too, and each suits different data.
Mean
Add the numbers and divide by how many there are. For 12, 15, 11, 15, 19, 8, 15 and 10 the total is 105, and 105 ÷ 8 = 13.125. The mean uses every value, so one very large or small number pulls it a long way.
Median
Put the numbers in order and take the middle one. With an even count there are two middle numbers, so the median is halfway between them. In order, the example is 8, 10, 11, 12, 15, 15, 15, 19; the middle two are 12 and 15, so the median is 13.5. Because it ignores how far out the extremes are, the median is used for house prices and incomes.
Mode
The value that appears most often: 15 in the example, three times. A list can have more than one mode, or none if every value appears once.
Range
The largest value minus the smallest: 19 − 8 = 11. It is a quick measure of spread. For a fuller measure, use the standard deviation calculator.
Exact answers
The numbers are added as exact fractions, so a long list of decimals does not pick up rounding errors. When the mean does not end, such as 10 ÷ 3, it is rounded to 10 significant digits and marked "about".
Formula and sources
- Mean, median and range as measures of center and variation: Common Core 6.SP.A.3 and 6.SP.B.5c.
- Median for an even count is the mean of the two middle values: NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1 (Measures of Location).
- Checked in test_maths.js: 12, 15, 11, 15, 19, 8, 15, 10 → mean 13.125, median 13.5, mode 15, range 11; 1, 2, 3, 4 → no mode; 0.1, 0.2 → mean exactly 0.15.