1. What is Percentile Rank?

The percentile rank indicates the percentage of scores in a distribution that a specific score is greater than or equal to. For a given z-score, it shows what percentage of the population falls below that value in a standard normal distribution.

2. How Does the Calculator Work?

The calculator uses the standard normal distribution formula:

Where:

• \( PR \) — Percentile rank (%)
• \( z \) — Standard score (z-score)
• \( \text{erf} \) — Gauss error function

Explanation: The formula converts a z-score to its corresponding percentile rank in a standard normal distribution.

3. Importance of Percentile Rank

Details: Percentile ranks are widely used in statistics, psychology, education, and standardized testing to interpret individual scores relative to a population.

4. Using the Calculator

Tips: Enter the z-score (positive or negative) to calculate its corresponding percentile rank. A z-score of 0 corresponds to the 50th percentile.

5. Frequently Asked Questions (FAQ)

Q1: What does a 90th percentile mean?
A: It means the score is higher than 90% of the population and lower than 10%.

Q2: What percentile is a z-score of 1.96?
A: Approximately 97.5th percentile (commonly used in 95% confidence intervals).

Q3: Can percentile rank be more than 100?
A: No, percentile ranks range from 0% to 100%.

Q4: What's the difference between percentile and percentile rank?
A: They're often used interchangeably, but technically percentile is the value below which a percentage falls, while percentile rank is the percentage.

Q5: How accurate is this calculator?
A: It provides results accurate to about 5 decimal places for the standard normal distribution.