Calculate standard deviation and variance

The mean is the sum of the observations divided by their count n. Population variance divides the sum of squared deviations from that mean by n. Sample variance divides it by n − 1. Standard deviation is the square root of variance. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5; population variance is 4 and population standard deviation is 2. The sample variance is 32/7 and sample standard deviation is about 2.1381.

Use 1.5 for a decimal, not 1,5. Commas are list separators, so 1,000 is interpreted as two observations, 1 and 0; enter 1000 for one thousand. Scientific notation such as 1e3 is accepted. Fractions, percentages, NaN and Infinity are rejected rather than silently omitted. Limits on characters and observations are shown beside the input and may be lower on low-memory devices.

The calculation uses an offset-centered Welford algorithm to reduce cancellation when observations are close together but large. It still uses floating-point numbers, so values beyond their representable precision cannot be recovered. Calculations that overflow, or underflow so that distinct observations would falsely appear to have zero variance, are rejected. Try expressing the values in a different consistent unit. Standard deviation has the same units as the observations; variance has squared units. Neither result alone proves normality or identifies an outlier.