Statistics Calculator
Paste a list of numbers to instantly find mean, median, mode, standard deviation, variance, and quartiles — with both sample and population values.
What this calculator computes
This tool parses your list of numbers and reports the full set of descriptive statistics. For variance and standard deviation it shows both the sample version (dividing by n − 1) and the population version (dividing by n), so you always pick the right one.
Mean (arithmetic average), median (middle value), and mode (most frequent value) describe where the data is centred.
Range, variance, and standard deviation measure how widely the values are dispersed around the mean.
Q1, Q2 (median), Q3, and the interquartile range (IQR = Q3 − Q1) split the data into four equal parts.
Sample vs population — which to use
Use population statistics (divide by n) when your data represents the entire group you care about. Use sample statistics (divide by n − 1, "Bessel's correction") when your data is a sample drawn from a larger population and you are estimating the population's spread. Most real-world inference uses the sample versions.
Population variance = Σ(x − μ)² / n
Frequently asked questions
How do you calculate the mean?
The mean (arithmetic average) is found by adding up all the numbers in your list and dividing by how many numbers there are. For example, the mean of 4, 8, 12 is (4 + 8 + 12) / 3 = 24 / 3 = 8. The mean is sensitive to outliers — one very large or very small value can pull it noticeably.
How do you find the median?
To find the median, first sort the numbers from smallest to largest. If there is an odd count of numbers, the median is the single middle value. If there is an even count, the median is the average of the two middle values. For 3, 7, 9, 11 (even count) the median is (7 + 9) / 2 = 8. The median is robust against outliers.
How do you find the mode?
The mode is the value that appears most often. To find it, count how many times each number occurs and pick the most frequent. A dataset can have one mode (unimodal), several modes (multimodal) if multiple values tie for the highest count, or no mode at all if every value is unique. This calculator lists all modes when there is a tie.
How do you calculate standard deviation?
Standard deviation is the square root of the variance. First find the mean, then square each value’s difference from the mean and add them up. For SAMPLE standard deviation divide that sum by (n − 1) and take the square root; for POPULATION standard deviation divide by n instead and take the square root. Sample SD is the usual choice when your data is a sample of a larger group.
What is the difference between variance and standard deviation?
Variance is the average of the squared deviations from the mean, so it is expressed in squared units. Standard deviation is simply the square root of the variance, which brings it back to the original units of your data and makes it easier to interpret. Both measure spread; standard deviation is usually reported because its units match the data.