Calculate the mean, median, mode and range of a set of numbers by entering values separated by commas or spaces.
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The mean is the sum of all values divided by how many there are, the familiar arithmetic average. The median is the middle value when the numbers are sorted in order (or the average of the two middle values if there's an even count), which isn't skewed by extreme outliers the way the mean can be. The mode is the value or values that appear most frequently in the data set.
The mean is useful for evenly distributed data, but a few extreme values can pull it away from what feels like a 'typical' value, for example, average household income is often much higher than the median due to a small number of very high earners. The median better represents a typical value in data sets with outliers or skewed distributions.
For the data set 4, 8, 6, 8, 15, 23 (6 numbers): the mean is (4+8+6+8+15+23) ÷ 6 = 64 ÷ 6 ≈ 10.67. Sorted, the values are 4, 6, 8, 8, 15, 23; with an even count of 6, the median is the average of the two middle values (8 and 8), which is 8. The mode is 8, since it's the only value that appears more than once (twice). The range is the highest minus the lowest: 23 − 4 = 19.
Forgetting to sort the values before finding the median, the median is the middle value of the sorted list, not the middle entry in whatever order you typed them.
Averaging the two middle values only when the count is even, and mistakenly doing the same for an odd count, an odd-count data set has one exact middle value, no averaging needed.
Assuming every data set has a mode, if every value is unique (appears exactly once), there is no mode, that's a valid and common result, not an error.
If two or more values tie for the highest frequency, this calculator lists all of them. If every value appears exactly once, it reports that there's no mode.
Enter numbers separated by commas, spaces, or both, for example '4, 8, 6, 8, 15, 23' or '4 8 6 8 15 23' both work.
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