ClarityHow to use this tool
- Enter sample mean, known population standard deviation, sample size, critical z value.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Sample mean | Numeric value. | 50 |
| Known population standard deviation | Numeric value. Must be greater than zero. | 10 |
| Sample size | Whole numbers only. Minimum: 1. Maximum: 1000000. | 100 |
| Critical z value | Numeric value. Must be greater than zero. | 1.95996398 |
Result for these sample inputs
48.04003601546 to 51.95996398454
- Margin of error
- 1.95996398
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Margin = z × population SD/√n. Interval = mean ± margin.
Using sample mean = 50, known population standard deviation = 10, sample size = 100, critical z value = 1.95996398454, the result is 48.04003601546 to 51.95996398454. Change these example inputs to match your task; use the method above to check each step.
What to keep in mind
Use the correct critical value and sampling assumptions. This is not a t interval for unknown population variance. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.
Methodology maintained by ClarityKit. How these tools are built and checked.