Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Merge Two Sample Summaries

Combine two disjoint sample summaries into one count, mean and sample variance.

Statistics workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaCount = n1+n2; Mean = (n1*m1+n2*m2)/(n1+n2); Sample Variance = ((n1-1)*s1**2+(n2-1)*s2**2+(m1-m2)**2*n1*n2/(n1+n2))/(n1+n2-1)
Sources and model references

Worked example

Inputs

First count
3 count
First mean
2 value
First sample SD
1 value
Second count
3 count
Second mean
5 value
Second sample SD
1 value

Expected results

Count
6 count
Mean
3.5 number
Sample Variance
3.5 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "n1": 3,
  "m1": 2,
  "s1": 1,
  "n2": 3,
  "m2": 5,
  "s2": 1
}

Accuracy and scope

Merges disjoint samples including the between-group mean difference; unlike pooled within-group variance. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.