MihsabaHow to use
Standard deviation measures how widely values spread around their mean. Mihsaba shows population and sample versions together so the effect of dividing by N versus n−1 is explicit, along with mean, variance and squared-deviation sum.
- Enter the data set.
- Calculate to find the mean and the sum of squared deviations from it.
- Compare population variance/deviation with the sample versions.
How it is calculated
Example
Example: 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 version divides by 7 instead of 8, so it is slightly larger.
Important notes
Use population statistics when the data contain every item in the group you are describing. Use the sample version when the observations are a sample from a larger population. Standard deviation alone does not make a value good, bad or risky without context.
Frequently asked questions
What is the difference between population and sample standard deviation?
Population divides squared deviations by N; sample divides by n−1 when estimating a larger population.
Why is variance the square of standard deviation?
Standard deviation is defined as the square root of variance, so variance equals standard deviation squared.
Can sample standard deviation be calculated from one value?
No. With n=1, n−1 is zero, so at least two sample observations are required.
Is this calculator free?
Yes. It is free to use and requires no account.