How to use the sampling distribution calculator
Prepare the values for this calculation
Calculate the sampling distribution standard error of a sample mean from population SD and sample size. 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
- Population mean μ: enter a finite number. Use the unit named in the label or selected above. Do not leave this required field blank.
- Population standard deviation σ: enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- Sample size n: enter a value at least 1 and no more than 1000000000 and a whole number. 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 Standard error of the mean first. With the unchanged example inputs, it is 2. 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 Population standard deviation σ from 12 to 13.2. The resulting Standard error of the mean is 2.2. 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.
Sampling Distribution Calculator formula
SE(x̄)=σ/√n.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Population mean μ | Number | 50 |
| Population standard deviation σ | minimum 0 | 12 |
| Sample size n | minimum 1; maximum 1000000000; whole number | 36 |
Worked example
Using the example inputs above, the standard error of the mean is 2.
- Standard error of the mean
- 2
- Sampling mean
- 50
- Sample size
- 36
Results and assumptions
The output uses the standard error of the mean convention and formula shown above. Match the entered units and source assumptions when comparing results.
Fix an input or unexpected result
Population mean μ is required. Enter population mean μ 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.