Average calculator
Type or paste your numbers, separated by commas, spaces or new lines. Every result updates as you type.
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Average (mean)
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- Median
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- Mode
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- Count
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- Sum
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- Lowest
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- Highest
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- Range
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- Std. deviation
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Mean, median and mode
The mean is what most people call the average: add the numbers and divide by how many there are. For test scores of 85, 92, 78, 92 and 88, the sum is 435 and there are 5 scores, so the mean is 435 ÷ 5 = 87. The median is the middle value once the numbers are sorted (78, 85, 88, 92, 92), here 88; with an even count it is halfway between the two middle values. The mode is the value that appears most often, here 92, which appears twice. If no value repeats there is no mode, and if two values tie, both are shown.
Examples
Results from the calculator for a few everyday lists:
| Numbers | Mean | Median | Mode | Range |
|---|---|---|---|---|
| Test scores: 85, 92, 78, 92, 88 | 87 | 88 | 92 | 14 |
| Weekly hours: 38, 40, 42, 40, 45, 40 | 40.83333 | 40 | 40 | 7 |
| House prices: 250,000 · 265,000 · 280,000 · 1,200,000 | 498,750 | 272,500 | none | 950,000 |
| Grades with weights: 90 (50%), 80 (30%), 70 (20%) | Weighted average 83 (plain average 80) | |||
The house prices show why the median matters: one expensive house pulls the mean up to 498,750, while the median of 272,500 is much closer to what a typical house costs. That is why incomes and home prices are usually reported as medians, as in the US Census Bureau's income figures. The grades row shows a weighted average: the part worth 50% counts two and a half times as much as the part worth 20%, so the result is 90 × 0.5 + 80 × 0.3 + 70 × 0.2 = 83.
Weighted average
Open Weighted average and enter one weight for each number, in the same order. Weights can be percentages (50, 30, 20), credits or hours (3, 4, 3), or anything else; they don't have to add up to 100, because the calculator divides by their total. For a GPA, enter each grade's points as the numbers and each course's credits as the weights.
Standard deviation and range
The range is the highest minus the lowest value. The standard deviation shows how spread out the numbers are around the mean: small when they are close together, large when they are scattered. The main figure is the sample standard deviation (dividing by n − 1), which is what spreadsheets' STDEV.S (and the older STDEV) gives and what you want when your numbers are a sample of something bigger. The population version (dividing by n, like STDEV.P) is shown under the result. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the population standard deviation is exactly 2 and the sample standard deviation is about 2.138. The difference shrinks as the list gets longer:
| Numbers | Mean | Sample (STDEV.S) | Population (STDEV.P) |
|---|---|---|---|
| 2, 4, 4, 4, 5, 5, 7, 9 | 5 | 2.13809 | 2 |
| Test scores above | 87 | 5.83095 | 5.21536 |
| Weekly hours above | 40.83333 | 2.40139 | 2.19216 |
| 10, 10, 10, 10 | 10 | 0 | 0 |
| 1, 100 | 50.5 | 70.00357 | 49.5 |
With only two numbers the two versions are far apart; with identical numbers both are 0.
Questions
How do I find the average of a set of numbers?
Add the numbers up and divide by how many there are. For 4, 8 and 9 the sum is 21 and there are 3 numbers, so the average is 21 ÷ 3 = 7.
How do I calculate a weighted average?
Type the weights in the second box, in the same order as the numbers. Each number is multiplied by its weight and the total is divided by the sum of the weights: 80 with weight 1 and 90 with weight 3 give (80 + 270) ÷ 4 = 87.5.
How do I find the median?
Put the numbers in order and take the middle one. With an even count, take the average of the two middle numbers: for 1, 3, 5 and 8 the median is 4. The Median line shows it for your numbers.
How do I average percentages?
If every percent is out of the same total, such as test scores out of 100, a plain average is right. If the groups are different sizes, use the size of each group as its weight, or the small groups count as much as the big ones.
How do I enter the numbers?
Any way you like: one per line (straight from a spreadsheet column), separated by commas, or by spaces. Numbers written with thousands separators, such as 1,250, are read correctly when the list is separated by spaces or new lines. Currency signs and % are ignored. Anything that isn't a number is skipped, and the calculator tells you what it skipped.
What is the difference between average and mean?
In everyday use they are the same thing: the sum divided by the count. Strictly, "average" can mean any typical value, including the median or the mode, which is why all three are shown.
How do I check this in Excel or Google Sheets?
Use =AVERAGE(A1:A10) for the mean, =MEDIAN(A1:A10), =MODE(A1:A10), =STDEV.S(A1:A10) for the sample standard deviation and =SUMPRODUCT(A1:A10, B1:B10)/SUM(B1:B10) for a weighted average with the weights in column B.