Statistics Calculator
Calculate mean, median, mode, standard deviation, variance, and more for a dataset. Free statistics tool.
About this calculator
Enter a list of numbers and get the count, sum, mean, median, mode, range, variance, standard deviation and minimum and maximum. The tool reports both population and sample variance and standard deviation, so you can use the one that matches your data.
It reads commas, spaces and line breaks, so you can paste a column straight from a spreadsheet.
How to use it
- Type or paste your numbers.
- Press Calculate.
- Read the table of statistics.
Definitions
Mean = Σx ÷ n. Population variance = Σ(x − mean)² ÷ n; sample variance = Σ(x − mean)² ÷ (n − 1). Standard deviation is the square root of the variance. The mode is the value that occurs most often, and the tool says None when all values are unique.
Worked example
Data: 12, 45, 7, 89, 34, 56, 23
| Mean | 38 |
| Median | 34 |
| Range | 82 |
| Population variance / SD | 693.142857 / 26.327606 |
| Sample variance / SD | 808.666667 / 28.437065 |
Tips and common mistakes
- Use the sample versions when you survey part of a population.
- The mean is pulled by outliers; compare it with the median.
- Sort your data to see the median and mode.
- Standard deviation has the same unit as the data, variance has its square.
- About 95% of normally distributed values lie within two standard deviations of the mean.
Frequently asked questions
What is standard deviation?
A measure of how spread out the numbers are around the mean.
Population or sample standard deviation?
Use sample when your data is a subset of a larger group.
What is variance?
The average squared distance from the mean.
What if the data has no mode?
The tool shows None.
What is the range?
Maximum minus minimum.
Can I paste from Excel?
Yes.