This calculator summarises a list of numbers: the mean (average), median, mode, range and standard deviation. Paste values separated by spaces, commas or newlines, and the statistics update as you type.
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Mean (average)
Enter some numbers Statistics appear here as soon as at least one valid number is entered.
Mean = Sum of values ÷ Count
The arithmetic average. It is sensitive to very large or very small values, which can pull it away from the median.
Median = middle value of the sorted list; Mode = most frequent value
The median splits the sorted list in half, taking the average of the two middle values for an even count. The mode is reported only when at least one value repeats; several values can share the top frequency.
σ = √(Σ(x − mean)² ÷ n); s = √(Σ(x − mean)² ÷ (n − 1))
Population standard deviation divides by the number of values; sample standard deviation divides by one less, which is the usual choice when the data is a sample. The sample figure is not shown for a single value.
A small data set with one repeated value.
The mean is 5, the median is 4.5 and the mode is 4. The population standard deviation is 2.
Values 1, 2, 2, 3, 3, 4.
The calculator reports 2 and 3 as modes instead of choosing one arbitrarily.
Text such as “abc” is ignored and listed in a warning, so one typo does not silently change the list. The statistics are calculated from the valid numbers only.
Population standard deviation assumes the list is the whole data set. Sample standard deviation corrects for estimating from a sample and is larger for small lists.
If every value appears once, there is no mode. If several values tie for the highest frequency, all of them are shown.
Both a dot and a comma are accepted. Commas can also separate list items, so “1, 2, 3” is three numbers while “1,5” is one number with a decimal comma.
The mean adds every value and divides by the count. The median is the middle value of the sorted list. Outliers pull the mean further than the median, so both are shown.
A mode requires at least one repeated value. When every number appears exactly once, the calculator reports “No mode” instead of inventing one.
Use population standard deviation when the list is the complete data set. Use sample standard deviation when the numbers are a sample used to estimate a larger population; it divides by n − 1.
Entries that cannot be parsed as numbers are ignored and named in a warning above the results. Statistics use only the valid numbers.
A single comma between digits, such as 1,5, is treated as a decimal comma. Other commas separate values, so 1,2,3 is read as three numbers. Spaces and newlines are unambiguous separators.
Up to eight decimal places, with trailing zeros removed. The underlying arithmetic keeps more precision, so the displayed figures do not accumulate rounding errors.