Confidence Interval Calculator
Calculate a confidence interval using a sample mean, standard deviation, sample size, and confidence level. This calculator estimates a range that is likely to contain the true population mean.
Enter the average of your sample data.
Enter the standard deviation of the sample or population.
Enter the number of observations in the sample.
Choose the confidence level for the interval.
How This Calculator Works
This calculator estimates a confidence interval for a mean by taking the sample mean and adding and subtracting a margin of error. The margin of error depends on the selected confidence level, the standard deviation, and the sample size.
Formula
Confidence Interval = Sample Mean +/- (Z Value * Standard Deviation / sqrt(Sample Size))
Example
If the sample mean is 72.5, the standard deviation is 8.4, the sample size is 50, and the confidence level is 95%, this calculator estimates the lower and upper bounds of the confidence interval around the mean.
Frequently Asked Questions
What is a confidence interval?
A confidence interval is a range of values that is used to estimate the true population mean based on sample data.
What does a 95% confidence level mean?
A 95% confidence level means the method used to build the interval would capture the true population mean about 95% of the time across repeated samples.
Why does sample size matter?
Larger sample sizes reduce the standard error, which usually creates a narrower confidence interval.
Why does higher confidence create a wider interval?
Higher confidence levels use larger critical values, which increases the margin of error and widens the interval.
What is the margin of error?
The margin of error is the amount added to and subtracted from the sample mean to create the confidence interval.