How it works
Variance of a weighted sum includes squared-weight variance terms and twice the weighted covariance. This form solves for first variable variance; enter the known quantities in Combination variance, First weight, Second weight, Second variable variance, Covariance of the variables.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Combination variance | 13 | Formula symbol: variance. Enter a numeric value. Use a non-negative value. |
| First weight | 1 | Formula symbol: a. Enter a numeric value. |
| Second weight | 1 | Formula symbol: b. Enter a numeric value. |
| Second variable variance | 9 | Formula symbol: vy. Enter a numeric value. Use a non-negative value. |
| Covariance of the variables | 0 | Formula symbol: cov. Enter a numeric 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.
- Combination variance
- 13
- First weight
- 1
- Second weight
- 1
- Second variable variance
- 9
- Covariance of the variables
- 0
Complete example results
- First variable variance
- 4
Reading the result
The result solves for first variable 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 first variable variance result?
Variance and covariance use matching squared units. Covariance magnitude cannot exceed the product of deviations. Zero correlation is not assumed.
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: online.stat.psu.edu