Statistics Calculator
How it works
The pasted text is first split on any run of commas, spaces or new lines and anything that is not a valid finite number is dropped, so a messy paste still turns into a clean list. From that list, mean is the sum divided by the count; median sorts the list and takes the middle value (or the average of the two middle values, for an even-length list); mode finds whichever value or values occur most often, reporting none if every value is unique.
Variance measures spread as the average squared distance from the mean. Population variance divides that total by the count; sample variance divides by one fewer, which corrects for a sample's mean being pulled toward its own data. Each standard deviation is simply the square root of its matching variance, back in the original units instead of squared ones. A single number has no meaningful spread, so its sample variance and standard deviation are shown as 0 rather than an undefined division by zero.
Frequently asked questions
Should I use sample or population standard deviation?
Use sample standard deviation when your numbers are a subset drawn from a larger group you have not fully measured — a handful of survey responses standing in for everyone, a batch of test scores from a bigger class. Use population standard deviation when your numbers ARE the entire group with nothing left out — every student in one specific classroom, every reading a sensor took last week. Sample standard deviation divides by one fewer than the count to correct for the fact that a sample's own mean sits closer to its own data than the true population mean would.
What does it mean if there is more than one mode, or none at all?
More than one mode (bimodal, trimodal, and so on) means those values are tied for being the most frequent in the list — none of them is "more the mode" than the others. No mode at all means every value in the list appears exactly once, so nothing repeats often enough to call it typical; that is reported as "None" rather than guessing at one of the numbers.
What counts as valid input?
Any numbers separated by commas, spaces, or new lines, in any mix — pasted spreadsheet columns, a comma-separated line, one number per line, all work. Anything that is not a valid number (stray text, an empty line from a double comma) is silently skipped rather than rejected, since a pasted list is rarely perfectly clean.