How it works
A chosen critical multiplier and known population deviation are scaled by the square root of independent sample size. This form solves for mean margin of error; enter the known quantities in Critical multiplier, Known population deviation, Independent sample size.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Critical multiplier | 2 | Formula symbol: z. Enter a numeric value. Must be greater than zero. Allowed range: 0.000001–100. |
| Known population deviation | 10 | Formula symbol: sigma. Enter a numeric value. Must be greater than zero. |
| Independent sample size | 100 | Formula symbol: n. Enter a numeric value. Use a whole number. Must be greater than zero. |
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.
- Critical multiplier
- 2
- Known population deviation
- 10
- Independent sample size
- 100
Complete example results
- Mean margin of error
- 2
Reading the result
The result solves for mean margin of error 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 mean margin of error result?
A normal-mean approximation and independent sampling are assumed. You choose the critical value; unknown sigma needs a separate t treatment. Required n is rounded up.
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: itl.nist.gov