Confidence Interval Calculator
Gives a range of plausible values for the true mean.
Confidence interval
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Margin of error —
Lower bound —
Upper bound —
Critical value —
Standard error —
Reading this —
The formula
CI = x̄ ± t × s ÷ √n
With a known population standard deviation, z replaces t. The t interval assumes the sample mean is close to normally distributed, which holds for roughly normal data or a fairly large sample.
What to watch out for
A higher confidence level or a more variable sample makes the interval wider. A larger sample makes it narrower.
Frequently Asked Questions
What is the 95% interval for a mean of 100, a standard deviation of 15 and 30 values?
94.399 to 105.6, using t with 29 degrees of freedom.
What z-values go with each confidence level?
1.645 for 90%, 1.96 for 95% and 2.576 for 99%.