THE NUMORIX GUIDE
How to use the Confidence Interval Calculator
Last reviewed September 14, 2026
What this calculator does
Compute standard error = SD/sqrt(n), select z for the confidence level, calculate margin = z*SE, and return [mean-margin, mean+margin].
Formula and method
Compute standard error = SD/sqrt(n), select z for the confidence level, calculate margin = z*SE, and return [mean-margin, mean+margin].
Variables and inputs
Sample Mean defaults to 100, Standard Deviation to 15, Sample Size to 100, and confidence to 95%. The selector supports 80, 90, 95, and 99 percent.
Worked example
For mean=100, SD=15, n=100, 95% confidence: SE=15/sqrt(100)=1.5; z=1.96; margin=2.94; interval = [100-2.94,100+2.94] = [97.06,102.94].
How to interpret the result
The interval is a procedure-based range for a population mean under the assumptions of the model. It is not a statement that a fixed parameter has a 95% probability after the interval is computed.
Common mistakes to avoid
Do not interpret 95% as 95% of individual observations, and do not use a sample standard deviation with an inappropriate small-sample z approximation without checking assumptions.
Assumptions and limitations
The engine always uses z critical values and does not switch to t values for small samples. It assumes the supplied SD and sampling model are suitable and does not include finite-population correction.
Practical use and checks
The Confidence Interval Calculator estimates a range around a supplied sample mean using standard deviation, sample size, and a selected z critical value. Enter mean 100, standard deviation 15, sample size 100, and confidence 95% as a check. The standard error is 1.5, the margin is about 2.94, and the interval should be approximately 97.06 to 102.94. Increasing the confidence choice to 99% should widen the interval, while increasing the sample size with the other inputs fixed should narrow it. Interpret the interval as the output of a repeated-sampling procedure under its assumptions. A 95% method means that, over many comparable samples, about 95% of intervals built this way would capture the target parameter; it does not mean there is a 95% probability that this already-computed fixed interval contains the parameter. The engine always uses z values and does not switch to a t distribution for a small sample with an estimated standard deviation. It also does not correct for finite populations, clustering, weighting, nonresponse, or a biased sample. A narrow interval can still be misleading if the data collection process is flawed. Record the unit, sampling design, confidence level, and source of the standard deviation with the result before using the range to approve a decision.