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. It's calculated using the normal distribution based on the mean and standard deviation of the data set.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( PR \) — Percentile rank (0-100%)
• \( x \) — The value being evaluated
• \( \text{mean} \) — Mean of the distribution
• \( \text{sd} \) — Standard deviation of the distribution
• \( \text{norm\_cdf} \) — Normal cumulative distribution function

Explanation: The formula converts the raw score to a z-score, then uses the normal distribution to find what percentage of values fall below that z-score.

3. Importance of Percentile Rank

Details: Percentile ranks are widely used in statistics, psychology, education, and other fields to compare individual scores to a reference population.

4. Using the Calculator

Tips: Enter the value you want to evaluate, the mean of the distribution, and the standard deviation. Standard deviation must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What does a percentile rank of 75 mean?
A: It means the score is equal to or higher than 75% of the scores in the reference population.

Q2: How is this different from a percentage?
A: A percentage is based on the maximum possible score, while a percentile rank compares a score to other scores in a distribution.

Q3: When is this calculation most appropriate?
A: When the data follows a normal distribution or when you want to compare a score to a normally distributed reference population.

Q4: What are the limitations?
A: The calculation assumes a normal distribution. For non-normal distributions, other methods may be more appropriate.

Q5: How accurate is this calculator?
A: It uses a precise approximation of the normal CDF function, accurate to about 5 decimal places.