Statistics Calculator
This free statistics calculator computes mean, median, mode, range, variance, and standard deviation, both population and sample, from any list of numbers. Paste or type your dataset and every figure updates instantly. Nothing you enter is sent anywhere or stored.
How to Use It
- Paste or type your numbers into the box, separated by commas, spaces, or new lines.
- Every statistic, mean, median, mode, range, variance, and standard deviation, updates instantly.
- No submit button, just edit the numbers and the results recalculate.
How It Works
Mean is the sum of every number divided by how many there are. Median is the middle value once the numbers are sorted, or the average of the two middle values when there's an even count. Mode is whichever value or values appear most often, and range is the difference between the largest and smallest values.
Variance measures how spread out the numbers are from the mean, and standard deviation is its square root, back in the same units as the original data. Population variance divides the sum of squared differences from the mean by the count of numbers; sample variance divides by one less than that count, a correction used when the dataset represents a sample rather than an entire population.
Formulas
mean = sum ÷ count
population variance = sum of (x − mean)² ÷ count
sample variance = sum of (x − mean)² ÷ (count − 1)
standard deviation = √variance
A worked example, the dataset 2, 4, 4, 4, 5, 5, 7, 9: mean 5, median 4.5, mode 4, range 7 (9 minus 2), population variance 4, population standard deviation 2, sample variance 4.57, and sample standard deviation 2.14. Everything runs client-side in your browser. Nothing you enter is sent anywhere or stored.
Frequently Asked Questions
What is the difference between population and sample variance/standard deviation?
Population statistics treat your dataset as the entire group you care about, dividing the sum of squared deviations by the count. Sample statistics treat your dataset as a sample drawn from a larger population, dividing by one less than the count instead (called Bessel's correction). If you have every value that matters (every student in a class, every day in a month), use population. If your numbers are a sample meant to estimate a larger group (a survey, a subset of measurements), use sample.
Why does mode sometimes show more than one number, or "No mode"?
Mode is whichever value or values appear most often. If two or more values are tied for the most frequent, all of them are shown. If every value in the dataset appears exactly once, there is no meaningful mode, so the tool says "No mode" rather than picking one arbitrarily or leaving the field blank.
Why is the median different from the mean?
Mean is the sum divided by the count, so a few very large or very small values can pull it away from where most of the data actually sits. Median is the middle value when the data is sorted (or the average of the two middle values, for an even-sized dataset), so it is less affected by outliers. For skewed data, median is often the more representative "typical" value; for evenly spread data, the two are usually close.
Why do I need to enter at least 2 numbers?
Sample variance and sample standard deviation divide by one less than the count of numbers. With a single number, that divisor would be zero, which is mathematically undefined, so this tool requires at least 2 numbers to calculate anything.
How should I format my dataset?
Separate numbers with commas, spaces, or new lines, in any combination. A column copied from a spreadsheet and a comma-separated list both work without reformatting.