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. None of the answer options is correct. b. the mean will be off center in the boxplot and above the median. c. the mean will be in the center of the boxplot. d. the boxplot is most likely symmetric about the mean.

First, we must inform that the median is not affected by outlier. Thus, there is possibility that a (some) student(s) score very high than others. This account for the reason why the mean value is higher than the median.

Since the mean is higher than the median, the score is skewed to the left! That is, majority of the students score low. Hence, we can say that the score is not exactly normal distributed.

NB:

Statistically the mean value given by the teacher is not significantly different from what the students obtained from the sample taken. This implies that, the sample is unbiased of the population mean as given by the teacher.