Assess how closely your z-score sample matches the standard normal model. Paste numbers separated by commas, spaces, or new lines. Get sample mean and variance, 95% intervals, and two-sided tests for μ = 0 and σ² = 1. Designed for stats learners, engineers, and data teams who need quick, interpretable checks.
μ = 0σ² = 1\bar{Z}, SE = 1/√ns² (unbiased)Enter at least one value to compute results.
1) What does this tool compute?
It summarizes your sample with mean and variance, builds confidence intervals, and runs two-sided tests for μ=0 and σ²=1 under the standard normal model.
2) Do I need large samples?
Larger samples produce tighter intervals and more reliable tests. Very small n can make variance estimates unstable.
3) Why two kinds of variance appear?
One uses the unbiased divisor (n−1) commonly reported as s². The other uses the population divisor n for reference.
4) Which interval is used for the mean?
Because σ is known (equal to 1 in the standard normal), a z-interval is used with standard error 1/√n.
5) How is the variance interval built?
It relies on the chi-square distribution of (n−1)s² when data are independent and normally distributed.
6) Can I paste values from a spreadsheet?
Yes. Separate entries by commas, spaces, or new lines. Non-numeric tokens are ignored.
7) What if my data are not standard normal?
The tests specifically check against μ=0 and σ²=1. If your process has other parameters, transform to z-scores first.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.