In a group of 200 student test scores, a score of S is located at the 75th percentile of t… — GRE General Test

In a group of 200 student test scores, a score of $S$ is located at the 75th percentile of the distribution. Which of the following statements must be true?

A
Score $S$ is equal to 75.
B
Approximately 75 students scored at or below $S$ .
Approximately 150 students scored at or below $S$ .Answer
D
Score $S$ is 75 percent greater than the average score of the distribution.
E
The standard deviation of the test scores is equal to 75.

Answer

Approximately 150 students scored at or below

S

The 75th percentile of a distribution indicates that approximately

75\%

of the data points lie at or below that value. For a group of 200 students,

75\%

of 200 is calculated as

0.75 \times 200 = 150

. Therefore, approximately 150 students achieved a score at or below

S

Step-by-Step Solution

Understand the definition of a percentile rank

The 75th percentile means that approximately

75\%

of all observations in the dataset are less than or equal to that score.

By definition, the

p

-th percentile represents the value below which

p

percent of the observations fall.

Calculate 75% of the total number of students

0.75 \times 200 = 150

students.

The dataset contains 200 total student scores, so

75\%

of 200 yields the number of students at or below score

S

Key Concept

Percentile Position

Estimated Time:45s

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