What is the difference between Confidence Interval and Margin of Error?

The Margin of Error is the 'radius' of the range. The Confidence Interval is the full range [Lower Bound, Upper Bound]. CI = Mean ± Margin of Error.

What does '95% Confidence' actually mean?

It means if you repeated the study 100 times, 95 of the resulting intervals would contain the true population mean. It describes the reliability of the method.

How do I make my Confidence Interval narrower?

You can decrease the Confidence Level (less certain) or, more effectively, increase the Sample Size (reduces standard error).

Does a wider interval mean better data?

No. A wider interval usually means either higher uncertainty (low sample size) or a higher required confidence level (e.g., 99% vs 90%).

What is the Z-value for 95% Confidence?

The critical Z-value for a 95% confidence interval is approximately 1.96, representing the number of standard deviations for the middle 95% of a normal distribution.

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IPL 2026

Confidence Interval Calculator

Calculate the range where a population mean is likely to fall. Estimate interval bounds with Z-values for various confidence levels.

Complete User Guide

Find your interval range with these steps:

Step 1: Enter the sample mean (average) and standard deviation.

Step 2: Enter the sample size (n).

Step 3: Select a confidence level (e.g., 95% or 99%).

Step 4: Click 'Calculate' to see the Margin of Error and the Lower/Upper bounds of the interval.

The Mathematical Formula

CI = x̄ ± Z * (s / √n)

The Confidence Interval (CI) is calculated using the sample mean and the margin of error:

- **Formula**: x̄ ± (Z * (σ / √n)) - **Margin of Error**: Z * (σ / √n) - **Standard Error**: σ / √n

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