Statistics Calculator

Separate the values with commas, spaces, semicolons or line breaks, in any mix, so you can paste a spreadsheet column directly. Use a period as the decimal separator, because a comma is treated as a separator between values. Scientific notation such as 1.5e3 is accepted.

Up to 10,000 numbers per calculation. Longer lists are rejected with a message instead of being cut silently. Any token that is not a number, such as a word or a unit, is reported by name so you can fix it.

Q1 and Q3 are the 25th and 75th percentiles using linear interpolation between the closest ranks, the method of Excel QUARTILE.INC and the R default. For 1, 2, 3, 4 this gives Q1 = 1.75 and Q3 = 3.25. Other textbooks use the median of each half, so results can differ slightly for small lists.

Population variance divides the sum of squared deviations by the number of values n and describes the data as the whole group. Sample variance divides by n - 1, which corrects the bias when your data is a sample from a larger population. Sample variance needs at least two values.

The mode is every value that occurs most often, together with how many times it occurs, so a list can have several modes. If every value appears only once, the tool says there is no mode. When more than ten values tie, the first ten are listed with a count of the rest.

The values are sorted and the middle one is taken. For an even count the median is the mean of the two middle values, so 1, 2, 3, 4 has a median of 2.5. The median is less affected by outliers than the mean.

The interquartile range is Q3 minus Q1, the spread of the middle half of your data. It ignores the lowest and highest quarter, which makes it robust against outliers. A common rule flags values more than 1.5 times the IQR beyond the quartiles as possible outliers.

Results are rounded to 6 decimal places by default, and you can choose anywhere from 0 to 15. Trailing zeros are removed, so 2.500000 appears as 2.5. Very large or very small values that would round to zero are shown in scientific notation instead.

Yes, negative values, decimals and numbers in scientific notation all work, in any order. The list does not need to be sorted, because the tool sorts a copy where needed for the median and quartiles. Duplicate values are kept and counted.

This tool reports both variances, and the standard deviation is their square root. The Standard Deviation Calculator shows the sample and population standard deviation directly, along with the standard error of the mean. Both tools accept the same list format.