This calculator computes common statistical values — count, sum, mean, median, mode, range, geometric mean, variance, and both population and sample standard deviation — for a set of numbers. Enter your values below, separated by commas, spaces, or line breaks.
The statistics calculator is a fast, all-in-one tool for describing a set of numbers. Enter your data and it instantly returns the most important descriptive statistics: the count, sum, mean, median, mode, range, geometric mean, variance, and both the population and sample standard deviation. It also sorts your data from smallest to largest so you can see the distribution at a glance. Whether you are a student checking homework, a teacher preparing examples, or a professional summarizing measurements, this calculator turns a raw list of numbers into a complete statistical summary in one click.
Descriptive statistics are the foundation of data analysis. Before running any advanced test or building any model, you first describe your data — where its center lies, how spread out it is, and whether any values repeat or stand out. This calculator computes all of those core measures at once, using the same standard formulas taught in statistics courses, so the results match textbooks and other reputable calculators exactly.
Type or paste your numbers into the box, separating them with commas, spaces, or line breaks — any combination works. Decimals and negative numbers are fully supported. Then click Calculate. The tool parses your list, ignores empty entries, and displays every statistic below. You need at least two numbers for a meaningful result. To start over, click Clear and enter a new set.
Each value below describes a different aspect of your data set. Together they give a complete picture of its center, spread, and shape.
The count is simply how many numbers are in your data set, usually written as n. It matters because many other formulas divide by the count, and because the reliability of a statistic generally improves as the count grows.
The sum is the total of all the values added together. It is the building block for the mean and a quick sanity check that all your data was entered.
The mean, or arithmetic average, is the sum of the values divided by the count: mean = Σx / n. It is the most familiar measure of central tendency, representing the "balancing point" of the data. The mean is sensitive to outliers — a single very large or very small value can pull it noticeably in one direction.
The median is the middle value when the data is sorted in order. If there is an odd number of values, it is the single center value; if there is an even number, it is the average of the two center values. The median is resistant to outliers, which is why it is often preferred to the mean for skewed data such as incomes or home prices.
The mode is the value (or values) that appears most often. A data set can have one mode, more than one mode (multimodal), or no mode at all if every value is unique. Unlike the mean and median, the mode can be used with non-numeric categories as well, and it is the only measure of center that must be an actual value from the data set.
The range is the difference between the largest and smallest values: range = maximum − minimum. It is the simplest measure of spread, giving a quick sense of how far apart the extremes are, though it ignores everything in between and is very sensitive to outliers.
The geometric mean is a different kind of average that multiplies all the values together and takes the nth root: GM = (x₁ × x₂ × … × xₙ)1/n. It is the right average to use for rates of change, ratios, and quantities that grow multiplicatively — investment returns, population growth, and index numbers, for example. Because it relies on multiplication, the geometric mean is only defined for positive numbers; if any value is negative the result is undefined (shown as NAN), and if any value is zero the geometric mean is zero.
Variance measures how far the data values spread out from the mean, and standard deviation is its square root, expressed in the same units as the data. A small standard deviation means the values cluster tightly around the mean; a large one means they are widely scattered. This calculator reports both the population and the sample versions of each, which differ in an important way explained below.
One of the most common points of confusion in statistics is the difference between population and sample standard deviation (and variance). The distinction is about what your data represents.
Dividing by n − 1 rather than n is known as Bessel's correction. It makes the sample variance an unbiased estimator of the true population variance, correcting for the fact that a sample tends to underestimate the spread of the population it came from. In practice, if your numbers are the complete set of everything you are studying, use the population values; if they are a sample used to draw conclusions about something larger, use the sample values. For large data sets the two are nearly identical, but for small ones the difference can be substantial.
Consider the default data set: 10, 2, 38, 23, 38, 23, 21, 23. There are eight values (count = 8), and they sum to 178, so the mean is 178 ÷ 8 = 22.25. Sorted, the data is 2, 10, 21, 23, 23, 23, 38, 38; with an even count, the median is the average of the two middle values, (23 + 23) ÷ 2 = 23. The value 23 appears three times, more than any other, so the mode is 23. The largest value is 38 and the smallest is 2, giving a range of 36. Summing the squared deviations from the mean gives 1059.5; dividing by n = 8 yields a population variance of 132.4375 and a population standard deviation of about 11.51, while dividing by n − 1 = 7 yields a sample variance of about 151.36 and a sample standard deviation of about 12.30. This is exactly what the calculator returns.
Descriptive statistics fall into two broad families. Measures of central tendency — the mean, median, and mode — describe where the "middle" of the data lies. Measures of spread (or dispersion) — the range, variance, and standard deviation — describe how spread out the data is around that middle. A complete summary needs both: knowing that the average test score was 75 tells you little without also knowing whether scores were tightly bunched around 75 or scattered from 40 to 100. That is why this calculator reports center and spread together.
Descriptive statistics are used in virtually every field:
Of all the numbers this calculator returns, the standard deviation is often the most informative — and the most misunderstood. It answers the question, "on average, how far is a typical value from the mean?" A standard deviation of zero means every value is identical; a large standard deviation means the data is very spread out. Because it is expressed in the same units as the original data (unlike variance, which is in squared units), it is easy to interpret directly. For data that follows the familiar bell-shaped normal distribution, the empirical rule is a handy guide: about 68% of values fall within one standard deviation of the mean, about 95% within two, and about 99.7% within three. That rule turns an abstract number into an intuitive sense of how unusual a given value is. When you see a data point more than two or three standard deviations from the mean, it is worth a closer look as a potential outlier or an especially notable result.
Type or paste your numbers into the box separated by commas, spaces, or line breaks. You can mix separators freely, and decimals and negative numbers are allowed. Then click Calculate.
Population standard deviation divides the sum of squared deviations by n and is used when your data is the entire group. Sample standard deviation divides by n − 1 (Bessel's correction) and is used when your data is a sample from a larger population. The calculator shows both.
The geometric mean is only defined for positive numbers because it relies on multiplication and taking a root. If any value in your data is negative, the result is undefined and shown as NAN. If any value is zero, the geometric mean is zero.
If every value appears exactly once, there is no mode and the calculator says so. If two or more values tie for the highest frequency, the data is multimodal and the calculator lists all of them along with how many times each appeared.
Sort the data, then take the two middle values and average them. For example, with the sorted set 2, 4, 6, 8, the median is (4 + 6) ÷ 2 = 5.
Yes. Variance is the square of the standard deviation, so standard deviation is the square root of variance. Just be sure to pair the matching versions: population standard deviation squared gives population variance, and sample standard deviation squared gives sample variance.
This Statistics Calculator is provided for educational and general informational purposes. Results are computed with standard descriptive-statistics formulas and displayed to high precision; round them as appropriate for your use. For formal research or high-stakes analysis, always verify calculations with dedicated statistical software.