1. What is a Median Confidence Interval?

A confidence interval for the median provides a range of values within which we can be confident (to a specified level) that the true population median lies. Unlike means, medians don't rely on distributional assumptions, making them robust for skewed data.

2. How Does the Calculator Work?

The calculator uses the bootstrap method to estimate the confidence interval:

Where:

• \( X_{(i)} \) — The i-th order statistic (sorted value)
• \( n \) — Number of observations
• \( z_{\alpha/2} \) — Critical value from normal distribution
• \( \alpha \) — 1 - confidence level (e.g., 0.05 for 95%)

Explanation: The method orders the data and selects symmetric positions to form the interval, adjusted by the confidence level.

3. Importance of Median Confidence Intervals

Details: Median CIs are particularly valuable when dealing with non-normal distributions, skewed data, or when outliers might unduly influence mean-based intervals.

4. Using the Calculator

Tips: Enter your numerical data as comma-separated values. Select your desired confidence level (90%, 95%, or 99%). The calculator will sort your data and compute the interval.

5. Frequently Asked Questions (FAQ)

Q1: When should I use median CI instead of mean CI?
A: Use median CIs when your data is skewed, has outliers, or isn't normally distributed.

Q2: How accurate is this method?
A: The bootstrap method provides good approximation for moderate to large sample sizes (n > 20).

Q3: What if my sample size is small?
A: For very small samples (n < 10), exact methods or tables may be more appropriate.

Q4: Can I use this for ordinal data?
A: Yes, the median CI can be used for ordinal data as long as the values can be ordered.

Q5: Why are my CI bounds equal to my data points?
A: This is expected with discrete data - the CI will span specific observed values.