Confidence interval calculator
Find a confidence interval for a population mean from summary statistics or raw data.
What a confidence interval says
A confidence interval gives a range of plausible values for a population mean based on your sample. A 95% interval means that if you repeated the sampling many times, about 95% of the intervals built this way would contain the true mean. It does not mean there is a 95% chance the mean is in this one interval.
t or z?
When you only know the standard deviation of your sample (the usual case), use the t distribution with n − 1 degrees of freedom. It has heavier tails than the normal curve, which makes the interval a little wider for small samples. If the population standard deviation σ is known, use z instead.
How the interval is built
The margin of error is the critical value times the standard error, where the standard error is the standard deviation divided by √n. The interval is the sample mean plus or minus the margin of error.
Making it narrower
A larger sample or a lower confidence level gives a narrower interval. Quadrupling the sample size cuts the margin of error roughly in half.