How this calculation works
A larger sample gets more weight because it contributes more degrees of freedom to the variance estimate.
sₚ = √[((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2)]A worked example
Equal sample sizes and standard deviations 2 and 4 give pooled variance 10.
Good to know
This estimates within-group spread and omits differences between group means.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Pool two within-group sample variances with degrees-of-freedom weights.
The primary result is labeled “Pooled standard deviation”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This estimates within-group spread and omits differences between group means.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
Equal sample sizes and standard deviations 2 and 4 give pooled variance 10.
Which rule does this calculator apply?
sₚ = √[((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2)]