OpenCourseWare on critical thinking, logic, and creativity

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1. The mean starting salary is HK$22,100 per month. The median starting salary is HK$15,000 per month. The reason they are so different is that student 00008 is an outlier, whose salary is five times larger than those of the other students. The salary of student 00008 is probably not typical of the graduates of this program; the other students' salaries are all fairly close to each other. In this case, the median value is probably the more informative way to summarize the data, since it is more likely to reflect the starting salary of the typical graduate from the program.

   Citing the mean in cases like this can be misleading. For example, in 1984 the University of Virginia stated that the average starting salary of students graduating from its program in rhetoric and communications was US$55,000 (HK$430,000) per year! This was not a lie; however, one of the graduates was a talented basketball player, Ralph Sampson, whose starting salary for the Houston Rockets NBA team was probably not representative of students in the program. (Source: Larry Gonick and Woollcott Smith (1993), The Cartoon Guide to Statistics. New York: HarperCollins.)

2. The mean mark is 41.7, and the median mark is 56. The reason they are so different is that there are three outliers--students who scored zero on the assignment, perhaps because they didn't complete the assignment for some reason. The policy requires that 16.3 (the required mean minus the actual mean) is added to each student's mark. This doesn't seem like the right response, since it results in all the students who completed the assignment getting marks which are significantly above the required mean of 58. In a situation like this, it might be better to use the median as a measure of the center of the data. Alternatively, you could disregard the outliers; among the students who completed the assignment, the mean mark is 59.6, which conforms with the policy.

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