Paste up to 10,000 numbers: mean, median, mode, variance, standard deviation for sample and population, plus MAD, CV%, and a histogram.
Your data set never leaves your device: every statistic and the chart are computed locally in your browser.
Which SD? Use the sample values (÷ n−1) when your numbers are a draw from a larger group; use the population values (÷ n) when they are the entire group. These are descriptive estimates, not professional statistical advice.
Standard deviation is a five-step story: find the mean; measure each value's deviation from it; square those deviations so negatives stop cancelling positives; average the squares; take the square root to return to the original units. The Formula card above walks those steps with your own numbers substituted in, so the symbols on the page are the arithmetic you just ran.
Ask whether your numbers are the whole story or a sample of a bigger one. Test scores for every student in your class: population SD, divide by n. Reaction times from 30 volunteers meant to speak for all adults: sample SD, divide by n-1. When in doubt, use the sample version — it is what statistics courses, scientific papers, and most spreadsheets' STDEV function default to, and it only differs by a small factor once n grows.
No — SD is one of the least robust common statistics because deviations are squared before averaging. A single 100 in the dataset 2, 3, 2, 4, 100 pulls the mean up and dwarfs every other deviation: SD jumps to about 42 while the median absolute deviation stays at 1. That is why this page also reports MAD; when SD and MAD disagree wildly, an outlier, not the data, is driving the number.
No, and mixing them up is a classic slip. SD describes how spread out your data points are. Standard error describes how uncertain your sample mean is as an estimate: SE = SD ÷ √n, so it shrinks as you collect more data while SD stays put. This tool gives you SD; for confidence intervals you need SE, which you can compute straight from the numbers shown here.
Because the deviations are measured from the sample mean, not the true population mean, and the sample mean has already been fitted to sit as close to your data as possible. That fit absorbs one degree of freedom, systematically shrinking the sum of squared deviations; multiplying by n/(n−1) undoes exactly that shrinkage, making the sample variance an unbiased estimate of the population variance.
No. The stats, the histogram, and the downloadable summary are all computed in your browser with plain JavaScript and a canvas. Paste up to 10,000 numbers if you like — they never leave your device, and no statistical estimates here are a substitute for professional advice.
If you just finished with Standard Deviation Calculator, the natural next steps are Grade Average Calculator, GPA Calculator, Scientific Calculator, or browse every tool in Daily Tools.