In a distribution of exam scores, what does it mean for a student’s score to be at the 16th percentile?

• A. The student’s score is 16% higher than the class average.
• B. About 16% of the scores are at or below the student’s score.
• C. About 16% of the scores are at or above the student’s score.
• D. The student’s score is 16 points above the minimum score.

Answer: (B)

Verified step by step guidance

1. Understand the concept of percentiles: A percentile indicates the relative standing of a value within a data set. Specifically, the p-th percentile is the value below which p percent of the data fall.
2. Interpret the 16th percentile: If a student's score is at the 16th percentile, it means that approximately 16% of all exam scores are less than or equal to that student's score.
3. Clarify common misconceptions: The 16th percentile does not mean the score is 16% higher than the average, nor does it mean the score is 16 points above the minimum score. It is about the position within the distribution, not the absolute difference.
4. Express the percentile mathematically: If \(X\) is the student's score, then \(P(X \leq x) = 0.16\), where \(P\) denotes the cumulative distribution function (CDF) of the exam scores.
5. Summarize the meaning: Being at the 16th percentile means the student scored better than or equal to about 16% of the students, and about 84% scored higher.