Compute mean, median, mode, standard deviation, variance, and other descriptive statistics from a data set.
Type or paste the numbers separated by commas.
See mean, median, mode, standard deviation, and variance.
Click copy to grab the calculated statistics summary.
Feed it a batch of numbers - quiz scores, response times, sensor readings - and it returns the standard summary statistics: count, mean, median, mode, range, variance, and standard deviation, in both the sample and population variants. Everything is computed from the values you enter, and nothing leaves the page. The most common surprise is that standard deviation comes in two flavors: dividing by n-1 (sample) or by n (population). They answer different questions, and using the wrong one is the usual source of mismatches with spreadsheets or published figures.
A concrete input and expected output from the current implementation.
Input
4, 8, 6, 5, 3, 8
Expected output
count 6; mean 5.67; median 5.5; mode 8; range 5; sample variance 4.27; sample standard deviation 2.07; population variance 3.56; population standard deviation 1.89
The six values sum to 34, so the mean is 34/6 = 5.67. Sorted, the list is 3, 4, 5, 6, 8, 8: the median is the average of the two middle values, (5 + 6)/2 = 5.5, and the mode is 8, the only repeated value. The squared deviations from the mean sum to about 21.33; dividing by 5 gives the sample variance 4.27, dividing by 6 gives the population variance 3.56, and the standard deviations are their square roots.
Each statistic is a direct formula over the entered values. The mean is the sum divided by the count. The median is the middle value of the sorted list, or the average of the two middle values when the count is even. The mode is the most frequent value, with every tied value reported if several tie. The range is the largest value minus the smallest.
The sum of squared deviations from the mean is divided by the number of values for the population variance, or by the number of values minus one for the sample variance; the standard deviation is the square root of either. The n-1 divisor, called Bessel's correction, is used when the numbers are a sample of a larger population, because dividing by n would on average underestimate how much that population varies.
Use the sample version when your numbers are a subset of a larger group you want to generalize about, such as twenty boxes measured to represent all boxes. Use the population version when the list is the complete group. When in doubt, the sample version fits most real-world uses; the two differ by a factor of sqrt(n/(n-1)).
Usually a convention mismatch. Excel's STDEV and STDEV.S return the sample standard deviation and STDEV.P returns the population version, so pick the matching mode here and the values agree to rounding. If they still differ, confirm the same values were entered in both places, since results depend on exactly which entries were counted.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate percentages, percentage change, and what percent one number is of another with step-by-step breakdowns.
Calculate tips and split bills between multiple people with customizable tip percentages and rounding options.
Calculate monthly payments, total interest, and generate amortization schedules for loans and mortgages.
Calculate Body Mass Index from height and weight with category classification and healthy range guidance.
Calculate sale prices, savings amounts, and final costs after single or stacked percentage discounts.
Convert between fractions, decimals, and percentages instantly with simplification and step-by-step work.