Confidence Interval Calculator | Estimate Population Mean
Easily calculate the confidence interval for a population mean when the standard deviation is unknown. Input sample data and confidence level for quick results.
Enter your sample data to calculate the confidence interval for the population mean. This tool is useful when you want to estimate the range within which the true population mean likely falls, based on your sample data.
Results
Confidence Interval:
This means we are % confident that the true population mean lies within this interval.
Confidence Interval Visualization
Understanding Confidence Intervals
A confidence interval is a range of values that's likely to include a population parameter with a certain degree of confidence. It's used in statistics to express the uncertainty in our estimate of a population parameter based on a sample.
Key Terms:
- Sample Mean (x̄): The average value calculated from your sample data.
- Sample Size (n): The number of observations in your sample.
- Sample Standard Deviation (s): A measure of the spread of data in your sample.
- Confidence Level: The probability that the confidence interval contains the true population mean. Common levels are 90%, 95%, and 99%.
For this calculator, we use the t-distribution because we are estimating the population mean when the population standard deviation is unknown. The formula involves the sample mean, sample standard deviation, sample size, and the appropriate t-value from the t-distribution table based on the chosen confidence level and degrees of freedom (n-1).
Learn more about confidence intervals on resources like Khan Academy or StatTrek.