Instant Statistics for Any Data Set
Paste or type a list of numbers and this statistics calculator instantly finds the mean (average), median, mode, range, minimum, maximum, sum and count. It also gives both the sample and population variance and standard deviation. Numbers can be separated by commas, spaces or new lines, so you can paste a column straight from a spreadsheet.
Mean, Median and Mode Explained
Example: for 4, 8, 15, 16, 23, 42, 8, the sorted list is 4, 8, 8, 15, 16, 23, 42. The mean is 116 ÷ 7 ≈ 16.57, the median is 15, the mode is 8 and the range is 38.
- Mean (average): add all the values and divide by how many there are.
- Median: the middle value when the numbers 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 one mode, several modes or no mode.
- Range: the largest value minus the smallest value.
Standard Deviation and Variance
Standard deviation measures how spread out the numbers are from the mean. A small value means the data is clustered together; a large value means it is spread out. Variance is the standard deviation squared.
Use the sample standard deviation (dividing by n − 1) when your numbers are a sample from a larger group, which is the usual case in surveys and experiments. Use the population standard deviation (dividing by n) when your data includes every member of the group. For the data set 2, 4, 4, 4, 5, 5, 7, 9, the population standard deviation is exactly 2.
Frequently Asked Questions
When should I use the median instead of the mean?
Use the median when the data has outliers or is skewed, like home prices or incomes. A few very large values pull the mean up, while the median stays representative of a typical value.
What if no number repeats?
Then the data set has no mode, and the calculator shows "No mode." If two or more values tie for the most appearances, all of them are listed.
Should I use sample or population standard deviation?
Use the sample standard deviation if your numbers are a sample drawn from a larger group. Use the population version only when you have data for the entire group. When in doubt, use the sample version.