Question

A student discovers that his grade on a recent test was the \(72^{\text{nd}}\) percentile. If 90 students wrote the test, then approximate number of students who received a higher grade than he did are:

• A. 65
• B. 25
• C. 72
• D. 71

Hint:

Exam Tip:
Percentiles:
• \(p\)-th percentile: \(p\%\) of data are below or equal.
• Number above = \((100 - p)\%\) of total.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The \(p\)-th percentile means that \(p\%\) of the observations are less than or equal to that value.

Step 2: Key Formula or Approach:
If a student is at the \(72^{\text{nd}}\) percentile, then \(72\%\) of the students scored less than or equal to him.
This means \(100\% - 72\% = 28\%\) of the students scored higher than him.

Step 3: Detailed Explanation:
Total students = 90.
Number of students who scored higher = \(28\%\) of 90.
\[ 0.28 \times 90 = 25.2 \approx 25 \] So, approximately 25 students scored higher.

Step 4: Final Answer:
Therefore, option (B) is correct.