Statistics Calculator
Paste a list of numbers to get the mean, median, mode, range, standard deviation and variance.
Descriptive statistics, sample and population · By Stuart Mathieson · Updated October 2026
Separate numbers with commas, spaces or new lines - you can paste a column from a spreadsheet.
Results
Mean (Average)
Median
Mode
Count
Sum
Range
Minimum
Maximum
Sample Standard Deviation (s)
Population Standard Deviation (σ)
Sample Variance (s²)
Population Variance (σ²)
Sorted values
Results are rounded to 6 decimal places.
What each statistic means
- Mean
- - the average: the sum of the values divided by how many there are.
- Median
- - the middle value when the values are sorted. With an even count, it is the average of the two middle values.
- Mode
- - the value that appears most often. A data set can have several modes, or none if every value appears once.
- Range
- - the largest value minus the smallest.
- Variance
- - the average squared distance of the values from the mean.
- Standard deviation
- - the square root of the variance, in the same units as the data - roughly, how far a typical value sits from the mean.
Worked example
For the values 2, 4, 4, 4, 5, 5, 7, 9:
- Count 8, sum 40, so the mean is 40 ÷ 8 = 5.
- The middle two values are 4 and 5, so the median is 4.5.
- 4 appears three times, so the mode is 4.
- The squared distances from the mean are 9, 1, 1, 1, 0, 0, 4 and 16, which add up to 32.
- Population variance = 32 ÷ 8 = 4, so the population standard deviation is 2.
- Sample variance = 32 ÷ 7 = 4.571429, so the sample standard deviation is 2.13809.
Sample or population standard deviation?
Use the population figures when your numbers are the whole group you care about - every student in one class, say. Use the sample figures when your numbers are a sample from a larger group and you want to estimate how spread out that larger group is.
The sample version divides by N − 1 instead of N (Bessel's correction). A sample tends to sit closer to its own mean than to the true population mean, so dividing by a slightly smaller number corrects for that. With large samples the two results are almost the same; with small ones the difference matters. If you're not sure, the sample standard deviation is the usual choice in statistics courses and research.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the average, the median is the middle value once the numbers are sorted, and the mode is the most common value. For 2, 4, 4, 4, 5, 5, 7, 9 they are 5, 4.5 and 4.
Should I use sample or population standard deviation?
Use population when your data is the whole group you're describing, and sample when it's a sample from a larger group. The sample version divides by N − 1 rather than N, which makes it slightly larger.
When is the median better than the mean?
When the data has outliers or is skewed. One very large value pulls the mean up, but barely moves the median - which is why incomes and house prices are usually reported as medians.
Can a data set have more than one mode?
Yes. If two or more values tie for the most appearances, they are all modes. If every value appears just once, there is no mode.
Sources
- Measures of Location - NIST/SEMATECH e-Handbook of Statistical Methods
- Measures of Scale - NIST/SEMATECH e-Handbook of Statistical Methods