A teacher returns an exam with possible scores ranging from 0 to 100. The students suspect that the majority of them performed poorly on the exam and request summary statistics. The teacher provides the mean, which was 72, as a summary statistic. A total of 400 students took the exam. Some of the students find the mean to be high, based on talking to other students. They take a random sample of 15 students, and they find that the mean equals 71.5 while the median equals 62. Based on this result, we conclude that:
A)the boxplot is most likely symmetric about the mean.
B)the mean will be in the center of the boxplot.
C)the mean will be off center in the boxplot and above the median.
D)None of the answer options is correct.

Question

Quizplus · Accepted Answer

Since the median is much lower than the mean, we can conclude that the distribution is skewed to the right, meaning that the mean is off center and above the median. Therefore, option C is the best choice. Options A and B are not valid because the information given does not allow us to determine the shape of the distribution or the position of the mean within the boxplot. Option D is not correct because we can make a conclusion based on the given information.

A Teacher Returns an Exam with Possible Scores Ranging from 0