2. In a Calculus class of 50 students, the highest exam score was 100, the mean was 72, the median was 71, and the mode was 75. Which of the following statements must be true?
Answer: C
The most frequently occurring score was 75
The statement that the most frequently occurring score was 75 must be true as it is directly supported by the provided mode of the exam scores. Since the mode represents the score that appears most often in a data set, it confirms that 75 is indeed the most common score among the students.
A) The lowest score was 70
This statement cannot be confirmed as true based on the given information. While the lowest score may indeed be 70, the data provided does not specify the lowest score, leaving it open to possibility. Therefore, it cannot be definitively stated that the lowest score was 70.
B) Twenty students had a score of 72 or greater
This statement does not necessarily hold true. Given the mean score of 72, it is possible that fewer than twenty students scored 72 or higher. Without additional data regarding the distribution of scores, we cannot conclude that twenty students reached this threshold.
D) More students had a score of 72 than 71
This statement is not guaranteed to be true. The median score is 71, which indicates that half the students scored below this value. It is conceivable that the number of students who scored 71 could equal or surpass those who scored 72, depending on the exact distribution of scores.
Conclusion
The correct answer, that the most frequently occurring score was 75, is definitively supported by the mode of the scores, which indicates its frequency. The other options either lack sufficient evidence from the data provided or are directly contradicted by the statistical measures given in the problem. Thus, only option C stands as a must-be-true statement based on the provided context.