Paste or type your numbers separated by commas, spaces or line breaks. You get the full set of descriptive statistics at once - count, sum, mean, median, mode, range, quartiles, variance and standard deviation - reported for both the sample and the population case so you can use whichever your assignment or analysis calls for.
The two differ only in the denominator: population variance divides by n, sample variance by n - 1. Use the sample figure when your numbers are a subset of a larger group you want to describe, which is nearly always. Use the population figure only when you have measured every member of the group - every employee, every item in a shipment.
The sample mean is calculated from the same data you are measuring spread against, so it sits closer to the observations than the true population mean does. That makes the deviations slightly too small. Dividing by n - 1 compensates. This is Bessel's correction, and its effect shrinks as the sample grows.
Standard deviation is sensitive to outliers, because deviations are squared. One extreme value can dominate it. The interquartile range - the middle 50% of the data - is not affected that way, so reporting both is worth doing whenever the data might be skewed.
Use the sample version, which divides by n-1, when your numbers are a sample drawn from a larger group and you want to estimate that group's spread. Use the population version, dividing by n, only when your numbers are the entire group. When in doubt, sample is the safer default.
Because the sample mean is itself estimated from the same data, deviations from it are slightly too small on average. Dividing by n-1 rather than n corrects that bias. This is called Bessel's correction.
Standard deviation is the square root of the variance. Variance is in squared units, which is awkward to interpret, so standard deviation is usually reported because it is back in the same units as the data.
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