Question

The mean score of a batch of students for the midterm exam was 78.2, and the standard deviation was 15.8. The batch's mean score on the final exam was 81.3, with a standard deviation of 4.5. Based on these statistics, which of the following can be interpreted?.

Answers:
a. The most common score on the final exam was lower than the most common score on the midterm exam.
b. The batch performed much better on the midterm exam than on the final exam
c. The mean revealed how spread out the batch's scores were
d. There was more variability in the scores of the midterm exam than of the final exam.

Answer 1

The correct interpretation is that there was more variability in the midterm exam scores compared to the final exam, as indicated by a higher standard deviation.

Step-by-step explanation:

The question pertains to the interpretation of statistical measures of a batch of students' performance on midterm and final exams, specifically focusing on mean scores and standard deviation. The correct interpretation based on the provided statistics is that there was more variability in the scores of the midterm exam than of the final exam.

This is understood by comparing the standard deviations: a higher standard deviation for the midterm exam (15.8) indicates that the scores were spread out more widely around the mean (78.2), while a lower standard deviation for the final exam (4.5) shows that the scores were closer to the final exam mean (81.3). The mean score does not reveal how spread out the scores were; that is the specific role of the standard deviation.