How to use the inverse variance calculator
Prepare the values for this calculation
Solve for a missing observation that makes the completed dataset have a specified sample variance. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Known values: use the same separators and value order as the example in the input table. Replace the example data with your own complete dataset.
- Target sample variance: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Missing value(s) first. With the unchanged example inputs, it is -0.309401076759 or 4.309401076759. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Target sample variance from 2 to 2.2. The resulting Missing value(s) is -0.476556749468 or 4.476556749468. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Inverse Variance Calculator formula
Using sample variance s²=[Σx²−(Σx)²/N]/(N−1), substituting one unknown produces a quadratic with up to two real solutions.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Known values | Text / numeric list | 1,2,3 |
| Target sample variance | minimum 0 | 2 |
Worked example
Using the example inputs above, the missing value(s) is -0.309401076759 or 4.309401076759.
- Missing value(s)
- -0.309401076759 or 4.309401076759
- Completed sample size
- 4
- Target sample variance
- 2
Results and assumptions
Uses the sample sample variance convention with denominator N−1 after adding one missing observation.
Fix an input or unexpected result
Target sample variance is required. Enter target sample variance using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.