Standard deviation calculator
Sample standard deviation divides by n−1 rather than n. The reason is that a sample mean is itself estimated from the same data, which slightly understates the true spread; dividing by one fewer corrects for it. Use the sample figure when your numbers are a sample of something larger, which is almost always. Use the population figure only when you genuinely have every member of the group.
Standard deviation measures spread around the mean. Sample standard deviation divides the summed squared deviations by n−1; population standard deviation divides by n. Use the sample figure unless you genuinely have every member of the group.
How to calculate standard deviation
Comparing mean against median is the quickest read on a data set anyone gets for free. When they are close, the data is roughly symmetric and the standard deviation describes it well. When the mean sits well above the median, a few large values are pulling it — income data being the classic case — and the standard deviation becomes a poor summary because it assumes the spread is symmetric. In that situation quartiles say more than a single deviation figure ever will.
Questions
Sample divides by n−1 to correct for estimating the mean from the same data. Population divides by n and needs the complete group.