Standard Deviation

How Standard Deviation works

Paste a list of numbers to get mean, median, both standard deviations and variance. Everything happens inside this page: the tool reads your input, runs the calculation or conversion locally, and hands the result back to you. Nothing is transmitted, because there is no backend to transmit it to.

That design choice is deliberate. Most free tool sites upload your files to a server, process them there, and quietly keep a copy. Toolcin cannot do that — the site is a set of static files. If your connection dropped the moment the page finished loading, every tool would still work.

Population or sample — the choice that changes the answer

The tool reports both. Population standard deviation divides the squared deviations by n; sample standard deviation divides by n − 1, the Bessel correction. The sample version is always slightly larger, and for a small dataset the difference is not academic.

Use the population figure when your numbers are the entire group you care about — every score in one class, every day of one month. Use the sample figure when the numbers are a subset used to estimate a larger population, which is the usual case in research and quality control.

What the number means in practice

Standard deviation is an average distance from the mean. A set with mean 20 and standard deviation 1 is tightly packed; the same mean with a standard deviation of 10 spans a wide range. Two datasets can share a mean and look nothing alike.

For roughly bell-shaped data, about 68% of values fall within one standard deviation of the mean and about 95% within two. That rule of thumb is only valid for bell-shaped distributions — for skewed data it overstates how much sits in the middle.

Reading the other outputs

Mean, median and range are shown alongside because a single summary statistic hides shape. If the mean and median differ noticeably, the data is skewed and the standard deviation is less informative than it looks.

Values can be separated by commas, spaces or semicolons, and non-numeric fragments are ignored rather than turned into zeros — a pasted table usually has headers, and silently counting them as 0 would corrupt every result.

Good to know

• Works offline once loaded, including on flights and in locked-down networks.
• No file size limit beyond your device's own memory.
• Free to use, with no account and no usage counter.
• Results are produced locally, so they are not logged or shared with anyone.

Questions