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math.confidence-interval-mean Calculator
Calculates the confidence interval for a population mean using the t-distribution and z-distribution, comparing both methods. The t-distribution is appropriate when the population standard deviation is unknown (which is almost always) — converges to z as n increases.
Inputs
Sample Mean
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Sample Std
Reference formula or conversion factor shown for context.
Sample Size
Number of data points collected. Larger samples give narrower confidence intervals. Rule of thumb: 30+ for most statistical tests.
Confidence Level Pct
How certain you want to be that the interval contains the true value. 95% is standard. Going to 99% widens the interval.
Results
confidence interval
Range within which the true population value lies at the stated probability. A 95% CI means: if you repeated the study 100 times, 95 of those intervals would contain the true value.
margin of error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
standard error SE
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
z-score for
Number of standard deviations a value is from the mean. |z| below 2: within normal range. |z| above 2: in the outer 5% of the distribution. |z| above 3: in the outer 0.3%.