Average calculator for a list of numbers: mean, median, mode, range, count and sum, with the sorted data and the middle values highlighted.
The 10 values add up to 849, so the mean is 84.9; the median is 86.5 and the mode is 92. The mean is 1.6 below the median, because the values below the median are, in total, farther from it than the values on the other side.
| Value | Count | Share of data | Note |
|---|---|---|---|
| 70 | 1 | 10 % | |
| 76 | 1 | 10 % | |
| 78 | 1 | 10 % | |
| 81 | 1 | 10 % | |
| 85 | 1 | 10 % | middle |
| 88 | 1 | 10 % | middle |
| 92 | 3 | 30 % | mode |
| 95 | 1 | 10 % |
The boxed value(s) sit in the middle of the sorted list.
92 appears 3 times, more often than any other value.
The mean is the sum of the values divided by how many there are. The median is the middle value once the data are sorted: the value at position (n + 1) ÷ 2 when n is odd, and the average of the two middle values when n is even. The mode is the value that occurs most often, and the range is the largest value minus the smallest.
For the 10 default quiz scores the sum is 849, so the mean is 84.9. Sorted, the 5th and 6th values are 85 and 88, which puts the median at 86.5; 92 appears three times and is the mode, and the range is 95 − 70 = 25.
Data can have several modes, all listed here, or none: when every value occurs equally often, no value is more typical than another. Standard deviation, quartiles and outliers are on the descriptive statistics calculator.
Checked against: Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849
Checked against: calculator.net mean, median, mode, range calculator worked example: mean 22.143, median 23, modes 23 and 38, range 36
Checked against: Calculator Soup mean, median, mode calculator example output: mean 16.75, median 15.5, mode 13, range 16, count 16, sum 268
Checked against: NIST StRD NumAcc1 certified mean 10000002; median and range by hand from the sorted values 10000001, 10000002, 10000003
Add the values and divide by the count for the mean: 10, 2, 38, 23, 38, 23, 21 sum to 155, and 155 ÷ 7 = 22.14. Sort them (2, 10, 21, 23, 23, 38, 38) and take the middle one, the 4th, for the median: 23. Count repeats for the mode: 23 and 38 each appear twice, so both are modes. The range is 38 − 2 = 36.
Sort the values and average the two in the middle, at positions n ÷ 2 and n ÷ 2 + 1. For the 16 values 9, 10, 12, 13, 13, 13, 15, 15, 16, 16, 18, 22, 23, 24, 24, 25, the 8th and 9th are 15 and 16, so the median is 15.5. This is the definition in the NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1.
Yes to both. NIST notes that the mode is not necessarily unique: 2, 3, 3, 5, 5, 8 has two modes, 3 and 5, and is called bimodal. When every value appears the same number of times, as in 4, 7, 9 or 1, 1, 2, 2, no value occurs more often than the others and the data have no mode.
Use the mean for roughly symmetric data without extreme values, the median when a few values are far from the rest, and the mode for categories or the most common size. One outlier moves the mean but not the median: for 3, 4, 5 the mean and median are both 4, but changing 5 to 50 lifts the mean to 19 while the median stays 4.
In everyday use "average" means the arithmetic mean, the sum divided by the count, and spreadsheet functions follow that: Excel's AVERAGE returns the mean. In statistics "average" is a looser word for any measure of center, so the median and mode are also called averages. When a report says "average" without saying which, it is almost always the mean.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “Quiz scores (default)” is checked against Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849.
NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of location (mean, median, mode); NIST Statistical Reference Datasets: univariate summary statistics (NumAcc1); Python statistics module: mean, median, multimode.
6 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
Descriptive statistics calculator: mean, median, mode, standard deviation, variance, quartiles, IQR, outliers, skewness and kurtosis, with a histogram.
Weighted average calculator: enter values with weights, one pair per line, for the weighted mean, sum of weights and each value's contribution.
Grade curve calculator: rescale a class's scores to a target mean and standard deviation, or add flat points, with z-scores and percentile ranks.
Grade calculator for weighted categories: your current course grade, and the score you need on the final exam or remaining work to reach a target.
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