How to use this calculator
Build a normal-approximation interval with a chosen z value. Enter sample mean, population standard deviation, sample size, critical z value. The result updates when you change an input. To compare two sets of inputs, save scenario A, then enter the second set; the result panel shows the difference.
Formula and limits
Margin = z × population standard deviation ÷ √n. Interval = mean ± margin. A z of 1.96 approximates 95% confidence under a normal model with known population standard deviation. Not a t interval.
Worked example
The following example uses the calculator’s starting values. It is an illustration of the method, not a recommended target.
| Input | Example value |
|---|---|
| Sample mean | 100 |
| Population standard deviation | 15 |
| Sample size | 100 |
| Critical z value | 1.96 |
Margin of error: 2.94
Interval: 97.06 to 102.94
Interpreting your result
Check whether your values represent a sample or an entire population. The sample-variance tools use n−1 in the denominator. Descriptive summaries cannot establish causation or validate how a sample was collected.
Comparing alternatives
Save the first result as scenario A, then change one input. The comparison shows the numeric difference; it does not label either result as better. Choose inputs that describe realistic alternatives. Values shown on screen are rounded, so calculations from rounded intermediate results may differ slightly.
Background reading
OpenStax Introductory Statistics. This is a subject reference, not an endorsement or independent review of Calcaven.