Confidence Interval Calculator
Find the range that likely contains the true mean of a population.
What the interval means
A confidence interval gives a range of plausible values for the true population mean, based on your sample. At 95% confidence, if you repeated the study many times, about 95% of the intervals built this way would contain the true mean.
Example
A sample of 100 with a mean of 50 and a standard deviation of 10 has a standard error of 1. At 95% confidence the margin of error is 1.96, so the interval is 48.04 to 51.96.
When to use it
This uses z values, which suit large samples (roughly 30 or more) or a known population standard deviation. For small samples, a t-based interval is wider and more appropriate. A bigger sample or a lower confidence level gives a narrower interval.
Frequently asked questions
What does 95% confidence mean?
It describes the method, not one interval. Ninety-five percent of intervals built this way capture the true value.
How do I make the interval narrower?
Collect a larger sample. The margin of error shrinks with the square root of the sample size.
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