Math
Standard deviation
Calculate population mean, variance and standard deviation for five values.
Calculators / Math / Pooled sample standard deviation
Pooled sample standard deviation calculator
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation.
On this page
Pooled standard deviation3.16
Degrees of freedom18
Calculator controls
How to calculate
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation.
Pooled standard deviation = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)); Degrees of freedom = n1+n2-2
Worked example
Sample count 1: 10; Sample standard deviation 1: 2; Sample count 2: 10; Sample standard deviation 2: 4.
Pooled standard deviation: 3.16 ; Degrees of freedom: 18 .
Assumptions and limits
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation. Pools within-group sample variance under an equal-variance assumption. This is not the standard deviation of all observations combined when group means differ.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation.
When this tool is useful
Pooled standard deviation = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)); Degrees of freedom = n1+n2-2
Understanding your inputs
| Input | What to enter |
|---|---|
| Sample count 1 | Enter a number of at least 2 and no more than 1000000000. |
| Sample standard deviation 1 | Enter a number of at least 0 and no more than 1000000000000. |
| Sample count 2 | Enter a number of at least 2 and no more than 1000000000. |
| Sample standard deviation 2 | Enter a number of at least 0 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Combine two sample standard deviations using their degrees of freedom as weights to estimate the shared within-group standard deviation. Pools within-group sample variance under an equal-variance assumption. This is not the standard deviation of all observations combined when group means differ.
How is the result calculated?
Pooled standard deviation = sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2)); Degrees of freedom = n1+n2-2