Standard deviation and variance of a data set.
Free to use, no sign-up required. Standard Deviation is one of 198 tools built into Xenition, alongside a chat that can use them for you.
Calculates the standard deviation, variance and mean of a data set, as either a whole population or a sample.
The tool finds the mean, then sums the squared distance of each value from it. Variance divides that sum by n for Population, or by n − 1 for Sample (Bessel’s correction). Standard deviation is the square root of the variance. Results show up to four decimal places.
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared distances sum to 32. As a population, variance is 32 ÷ 8 = 4 and standard deviation is 2. As a sample, variance is 32 ÷ 7 = 4.5714 and standard deviation is 2.1381.
Use Population when your list contains every member of the group, such as every score in one class. Use Sample when the list is a subset used to estimate a larger group, which is the usual case in surveys and experiments.
A sample tends to sit closer to its own mean than the whole population does, which understates the spread. Dividing by n − 1 instead of n corrects for that.
You do not have to open Standard Deviation to use it. Ask Xenition in plain language and it runs the right tool, then carries the answer into whatever you are working on — a document, a spreadsheet, a deck.