Standard Deviation Calculator
Calculate the mean, variance, and standard deviation (both population and sample) for a set of numbers.
Calculate Standard Deviation
About this Calculator
Calculate the mean, variance, and standard deviation (both population and sample) for a set of numbers.
Formula & Calculations
Formula
Population SD: σ = √(Σ(xᵢ - μ)² / N), Sample SD: s = √(Σ(xᵢ - x̄)² / (n - 1))Where:
- μ=Population mean (average of all values in the population)
- x̄=Sample mean (average of all values in the sample)
- σ=Population standard deviation
- s=Sample standard deviation
- N=Number of values in the population
- n=Number of values in the sample
Assumptions
- Numbers should be separated by commas or spaces.
- Non-numeric entries are ignored.
- Sample standard deviation uses n-1 (Bessel's correction) for an unbiased estimate.
Calculation Examples
Example 1
The data set has a mean of 18 with a relatively tight spread around the average.
Example 2
Evenly spaced values produce a standard deviation that reflects the spread of the dataset.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation divides by N (total number of items) and is used when you have data for the entire group. Sample standard deviation divides by n-1 (Bessel's correction) and is used when your data represents a sample of a larger population.
What does a high standard deviation indicate?
A high standard deviation means the data points are spread out over a wide range of values. A low standard deviation indicates that the data points tend to be close to the mean.