Statistics
Confidence interval calculator
Estimate a confidence interval for a mean using the sample mean, standard deviation, sample size, and confidence level.
Lower limit
47.64804322
Upper limit
52.35195678
Margin of error
± 2.351956783
Standard error
1.2
Interval representation
47.6480432252.35195678
This calculation uses a Z critical value from the normal distribution. It is appropriate when the population standard deviation is known or the sample is large enough. For small samples with an estimated standard deviation, a t-distribution is usually preferred.
Frequently asked questions
What does the interval represent?
It is a range calculated around the sample mean using a given confidence level and statistical model.
What happens when the confidence level increases?
The interval usually widens because it needs to cover a larger range.
What happens when the sample is increased?
The standard error decreases and, all else being equal, the interval becomes narrower.