Standard Deviation Calculator
About Standard Deviation Calculator
Calculate mean, variance, and standard deviation from a list of values.
How to Use
Calculate mean, variance, and standard deviation from a list of values. Fill in Values, then review the calculated Count, Mean, Population standard deviation, Sample standard deviation, Population variance, Sample variance, Selected standard deviation, Selected variance, and Method used.
- Open the calculator : Use Standard Deviation Calculator from the Math category.
- Check the inputs : Review the required values and any optional settings.
- Read the formula : Use the formula and notes below to understand how the result is produced.
Common Questions
What formula does the Standard Deviation Calculator use?
Population standard deviation = ?(sum((x - μ)^2) / n). Sample standard deviation = ?(sum((x - x̄)^2) / (n - 1)).
What does standard deviation actually tell you?
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation means most data points are grouped closely around the average (mean), while a high standard deviation indicates the data is spread out over a much wider range.
What is a normal distribution (bell curve)?
In a normal distribution, roughly 68% of all data points will fall within one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will fall within three. This is known as the Empirical Rule.
Inputs
- Values
Outputs
- Count
- Mean
- Selected standard deviation
- Selected variance
- Population standard deviation
- Sample standard deviation
- Population variance
- Sample variance
- Method used
Formula
Population standard deviation = sqrt(sum((x - μ)^2) / n). Sample standard deviation = sqrt(sum((x - x̄)^2) / (n - 1)).