Purpose: Find both population and sample standard deviation, variance and mean for any list of numbers.
Standard Deviation Calculator
The Standard Deviation Calculator measures how much a set of numbers varies around its mean, giving both population and sample standard deviation with the variance and step-by-step working.
How it is calculated
Standard deviation is the square root of the variance. The tool finds the mean, measures how far each value sits from it, squares those differences, averages them (dividing by N for a population or N−1 for a sample), and takes the square root. Showing each step makes it a genuine study aid for statistics students.
Population or sample?
Choose population when your numbers are the complete set you care about, and sample when they are a subset used to estimate a bigger group. The sample version (dividing by N−1) gives a slightly larger, unbiased estimate - this is the correct choice for most real-world experiments and surveys.
Frequently Asked Questions
What does a high standard deviation mean?
It means the values are widely spread out from the average. A low standard deviation means they cluster closely around the mean.
Why does sample standard deviation divide by N−1?
Dividing by N−1 (Bessel's correction) removes bias when estimating the spread of a whole population from a sample, giving a more accurate estimate.
What is the link between variance and standard deviation?
Standard deviation is simply the square root of the variance, expressed in the same units as your original data.
Does it show the working?
Yes. It displays the mean, squared deviations, variance, and final standard deviation so you can follow every step.
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