Looking for a standard deviation calculator population and sample? This free tool gives you mean, median, variance and both population and sample deviation. Just enter your numbers and press Calculate — results are instant.
Standard deviation measures how spread out numbers are around their average. First find the mean, then measure how far each number sits from it, square those distances, average them (that is the variance), and take the square root. A small standard deviation means the numbers cluster tightly; a large one means they are spread out. The population version divides by the count; the sample version divides by count minus one, which is the version to use when your numbers are a sample of something bigger.
Example: Numbers: 5, 10, 15, 20, 25
Standard Deviation (Population): 7.0711
Use population when your numbers are the whole group you care about. Use sample when they are a sample of something bigger — a survey, an experiment, a few measurements. For most real-world data, sample is the right choice.
How spread out your numbers are. A small value means the numbers cluster tightly around the average; a large value means they are scattered. Two sets can have the same average and very different standard deviations.
Variance is the average of the squared distances from the mean; standard deviation is its square root. Variance is in squared units, which are hard to picture, so standard deviation is the one people usually quote.
Every number in the list is identical — there is no spread at all.