Calculators
Statistics Calculator
Mean, median, mode, variance, standard deviation, and more.
Statistics Calculator tool
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About This Tool
Summarize a set of numeric observations in one place. This calculator accepts a list of numbers and reports common descriptive statistics: count, sum, arithmetic mean, median, mode, minimum, maximum, range, population variance and standard deviation, plus sample variance and standard deviation when at least two observations are available. Everything is calculated locally with standard browser numbers, making it useful for homework checks, quick data summaries, measurements, experiments, and everyday numeric comparisons.
How To Use It
- Paste or type your observations into the Numbers field. You can separate them with commas, spaces, semicolons, or new lines.
- Review the automatically calculated summary. Decimals and negative values are accepted.
- Choose the population or sample variance/standard-deviation result according to what your data represents, and use Copy to save the complete summary.
Examples
Small score set
For 1, 2, 2, 3, 4, the mean is 2.4, median is 2, mode is 2, and range is 3.
Even number of observations
For 1, 2, 3, 4, the median is halfway between the two middle sorted values: (2 + 3) / 2 = 2.5.
Multiple modes
For 1, 1, 2, 2, 3, both 1 and 2 occur most frequently, so both are reported as modes.
No repeated value
For 5, 8, 12, every value appears once. The calculator reports no mode rather than listing every observation as a mode.
Useful Notes
Mean, median, and mode
The arithmetic mean is the sum divided by the number of observations. The median is the middle value after sorting, or the average of the two middle values when the count is even. The mode is the value or values with the greatest frequency; this tool reports no mode when every value occurs exactly once.
Population vs. sample variance
Population variance divides the sum of squared deviations from the mean by N and describes the complete population supplied. Sample variance divides by N − 1, the usual Bessel correction used when the observations are a sample intended to estimate variability in a larger population.
Standard deviation
Standard deviation is the square root of variance, so it is expressed in the same units as the original observations. Smaller values indicate observations are more tightly clustered around the mean; larger values indicate greater spread.
Precision and limits
Calculations use JavaScript double-precision floating-point numbers. This is appropriate for ordinary descriptive-statistics work, but it is not arbitrary-precision statistical software. Extremely large magnitudes can overflow or lose precision. If the sum or a derived statistic overflows, the calculator shows an error instead of displaying an infinite result. Smaller magnitudes or a smaller spread may bring the calculation within range.
FAQ
Which standard deviation should I use?
Use population standard deviation when your entered values are the full population you want to describe. Use sample standard deviation when the values are a sample used to estimate a larger population's variability.
Why is sample variance unavailable for one value?
Sample variance divides by N − 1. With one observation that denominator is zero, so a sample variance cannot be calculated.
Does the calculator support negative numbers and decimals?
Yes. Negative finite values and decimals are valid observations.
Does the order of my numbers matter?
No. Sum, mean, variance and standard deviation do not depend on order, and the calculator sorts a copy of the data when finding the median without changing your input.