Final answer:
The percentile rank indicates the position of a score within a large population, where a score in the 90th percentile means that 90% of scores are the same as or lower and 10% are higher. Percentiles are used for comparison, such as in university admissions. They are calculated by ordering the data and finding the score below which a certain percentage of the data falls.
Step-by-step explanation:
The percentile rank is a statistical measure that indicates the relative standing of a score within a large population. For example, if you have a score in the 90th percentile, this does not mean that you've achieved 90% on an exam. It means that 90 percent of test takers have scores that are the same as or lower than yours, and conversely, 10 percent have scores that are higher. Percentiles are useful for comparisons in various contexts, such as college admissions, where a university might only accept students with SAT scores in the top 25% (above the 75th percentile).
To calculate percentiles, you need to order the data from smallest to largest. Remember that percentiles divide the data into 100 equal parts, while quartiles divide the data into four parts. The median (50th percentile) divides the ordered data set into two equal halves, with 50 percent of the data falling below and 50 percent above. To calculate specific percentiles like the 90th or 70th, you will have to find the score below which falls 90 or 70 percent of the data, respectively.
Example Interpretation
In a given context, say a 20-question math exam, if the 70th percentile is 16, this means that 70 percent of students answered 16 or fewer questions correctly, while 30 percent answered more than 16 questions correctly.