For many sets of measurements the median lies between the mode and the mean. But this is not always so.

(A) In a class of seven students, the scores on an exam were 52, 89, 89, 92, 93, 96, 99. Show that the mean is less than the mode and that the mode is less than the median.

(B) Construct hypothetical sets of exam scores to show that all possible orders among the mean, median, and mode can occur.