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About this tool
Paste any list of numbers to get the mean, median, mode, range, geometric and harmonic mean, quartiles and outliers, plus a weighted average.
This average calculator works out the mean, median, mode and range of any list of numbers you paste or type, whether they are separated by commas, spaces, tabs or new lines. Alongside the usual averages it gives the sum, count, minimum and maximum, geometric and harmonic means, sample and population standard deviation, quartiles, a 10% trimmed mean and a warning for possible outliers using the 1.5 × IQR rule. A dot plot or histogram marks the mean and median, and the Working card shows the sorted list with the middle values highlighted. The Weighted average tab handles grades, credits or prices with a weight for each value. Your data stays in your browser.
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Paste or type your data into the Numbers box — commas, spaces, new lines, tabs and semicolons all work — or tap an example such as Test scores.
If your data uses commas as thousands (1,234) or as decimal points (1,5), change Commas in the data, and pick Show results to 0–6 decimal places if you want rounding.
Read the Results card for the mean, median, mode and range plus the geometric mean, harmonic mean, standard deviation and quartiles, then check the Chart and Working cards.
For grades or credits, open the Weighted average tab, enter each Value with its Weight, and use Add row for more; the table shows every w × x product.
Numbers are pulled from messy text — currency signs, units and labels are skipped — and you choose whether commas separate values, mark thousands or are decimal points.
Mean, median, mode (including several modes), geometric mean for growth rates, harmonic mean for rates and speeds, trimmed mean and root mean square.
Range, quartiles, IQR, variance and standard deviation in sample and population form, with an automatic outlier check.
A dot plot or histogram with mean and median lines, the sorted data with the median highlighted, and copyable results.
| Average | How it is found | Working | Result |
|---|---|---|---|
| Mean (arithmetic) | Sum ÷ count | 30 ÷ 6 | 5 |
| Median | Middle value when sorted | (3 + 5) ÷ 2 | 4 |
| Mode | Most frequent value | 3 appears twice | 3 |
| Range | Largest − smallest | 10 − 2 | 8 |
| Geometric mean | nth root of the product | ⁶√(2 × 3 × 3 × 5 × 7 × 10) | 4.298 |
| Harmonic mean | Count ÷ sum of reciprocals | 6 ÷ (1/2 + 1/3 + …) | 3.728 |
For positive numbers the harmonic mean is never larger than the geometric mean, which is never larger than the arithmetic mean; they are equal only when every value is the same.
The everyday average is the arithmetic mean: add all the numbers together and divide by how many numbers there are. For 4, 8 and 15 the sum is 27 and there are 3 numbers, so the average is 27 ÷ 3 = 9. The calculator shows this sum and division in the Working card so you can check it.
The mean is the sum divided by the count. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. For 2, 3, 3, 5, 7, 10 the mean is 5, the median is 4 and the mode is 3. The median and mode are not affected by one very large or very small value, but the mean is.
Sort the numbers from smallest to largest. If there is an odd count, the median is the single middle value: for 7 values it is the 4th. If there is an even count, average the two middle values: for 2, 3, 3, 5, 7, 10 the middle pair is 3 and 5, so the median is 4. The calculator highlights the middle values in the sorted list.
If every value appears only once, the data set has no mode. If two or more values tie for the highest count, all of them are modes — a set with two is called bimodal. For 1, 1, 2, 2, 3 the modes are 1 and 2. When every value appears equally often, such as 4, 4, 6, 6, there is also no single mode.
Multiply each value by its weight, add up those products, and divide by the total of the weights. For grades of 92, 85 and 78 worth 20%, 30% and 50%: 92 × 20 + 85 × 30 + 78 × 50 = 8,290, and 8,290 ÷ 100 = 82.9. Weights do not have to add up to 100; credits or quantities work the same way.
Use the median when the data is skewed or has outliers, such as house prices or incomes, where a few very large values drag the mean up. For 12, 15, 11, 14, 13, 12, 16 and 58 the mean is 18.875 but the median is 13.5, which better describes a typical value. For symmetric data without outliers the two are close.
The geometric mean multiplies the values and takes the nth root, so it suits quantities that multiply, like growth rates and investment returns. Growth factors of 1.10 and 0.90 have an arithmetic mean of 1.00 but a geometric mean of about 0.995, which correctly shows a small overall loss. It is only defined here when every value is greater than zero.
The harmonic mean is the count divided by the sum of the reciprocals. It gives the right average for rates over equal amounts, such as speed over equal distances: driving 60 km at 40 km/h and 60 km at 60 km/h averages 48 km/h, not 50. It is also used for price-earnings ratios and the F1 score.
It uses the interquartile range rule. The first quartile Q1 and third quartile Q3 are found by the median-of-halves method and IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged as a possible outlier. This is a guide, not proof that the value is wrong; check it against how the data was collected.
Use the population formula, dividing by n, when your numbers are the whole group you care about, such as every student in one class. Use the sample formula, dividing by n − 1, when the numbers are a sample from a bigger group and you want to estimate that group's spread. Both are shown; the sample value is slightly larger.
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