Confidence Interval Calculator
Calculate the confidence interval for a population mean. Determine the margin of error and range where the true population parameter likely falls.
Inputs
Results
Margin of Error (Β±)
1.96
Lower Bound48.04
Upper Bound51.96
Standard Error1
Z-Score Used1.96
Interval Width3.92
InterpretationWe are 95% confident that the true population mean lies between 48.04 and 51.96
How to Use This Calculator
- Enter your Sample Mean (xΜ) β the average of your collected data points.
- Enter the Standard Deviation (Ο) of your sample and the Sample Size (n, number of observations).
- Choose a Confidence Level: 90%, 95%, or 99% β higher confidence produces a wider interval.
- The calculator uses the z-score for the chosen level (e.g., 1.96 for 95%) and computes: margin of error = z Γ (Ο / βn).
- Lower Bound and Upper Bound define the range where the true population mean is expected to fall with the stated confidence.
- Increase sample size to narrow the interval without changing confidence level.
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Formula
CI = xΜ Β± z Γ (Ο / βn)Related Calculators
Z-Score Calculator
Calculate the z-score (standard score) for any value in a normal distribution. Find the percentile ranking and probability associated with your data point.
Sample Size Calculator
Determine the required sample size for your survey or study. Calculate how many responses you need for statistically significant results.
Standard Deviation Calculator
Calculate the mean, median, standard deviation, and variance for a set of numbers. Supports both population and sample calculations.
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