How the standard Deviation Calculator works
Standard deviation measures the typical distance of each value from the mean: square every deviation, average the squares (dividing by n minus 1 for a sample), and take the square root. Small deviation means tightly clustered data, large means spread.
s = √( Σ(x − mean)² ÷ (n − 1) )
Example: the set 12, 15, 14, 10, 8, 12, 16, 11 has a mean of 12.25 and a sample standard deviation of about 2.66.
Frequently asked questions
Sample or population, which do I pick?
Population if you have every member of the group you care about, sample if your data represents a larger group. Almost all real-world data sets are samples, hence the n minus 1 default.
What does one standard deviation mean in practice?
For roughly bell-shaped data, about 68% of values fall within one deviation of the mean, 95% within two, and 99.7% within three.
Standard deviation vs variance?
Variance is the deviation squared, which puts it in squared units. Standard deviation returns to the original units, which is why it is the number people quote.