How it works
Within-group sums of squares plus the between-mean contribution are divided by the merged sample’s n−1 denominator. This form solves for merged sample variance; enter the known quantities in First group size, Second group size, First group mean, Second group mean, First group sample deviation, Second group sample deviation.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| First group size | 5 | Formula symbol: n1. Enter a numeric value. Use a whole number. Must be greater than zero. |
| Second group size | 5 | Formula symbol: n2. Enter a numeric value. Use a whole number. Must be greater than zero. |
| First group mean | 10 | Formula symbol: m1. Enter a numeric value. |
| Second group mean | 20 | Formula symbol: m2. Enter a numeric value. |
| First group sample deviation | 2 | Formula symbol: s1. Enter a numeric value. Use a non-negative value. |
| Second group sample deviation | 2 | Formula symbol: s2. Enter a numeric value. Use a non-negative value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- First group size
- 5
- Second group size
- 5
- First group mean
- 10
- Second group mean
- 20
- First group sample deviation
- 2
- Second group sample deviation
- 2
Complete example results
- Merged sample variance
- 31.33333333
Reading the result
The result solves for merged sample variance from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the merged sample variance result?
Summaries need disjoint observation groups and the same unit. This describes merging raw observations, not the equal-variance pooled estimate.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: doi.org · online.stat.psu.edu