mar10 - Illinois Institute of Technology Department of...

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Illinois Institute of Technology Department of Computer Science Lecture 13: March 10 CS 330 Discrete Mathematics Spring Semester, 2008 1 How indicative of “real life” is the average? The mean or expected value is often not enough when we are trying to draw some meaningful conclusions about the nature of a distribution. Suppose you were told that the average score on the CS 330 midterm was 50, you still do not know if everyone in the class scored a 50, or if half the class scored 0 and the other half 100, and so on. In our analysis of the algorithm for determining the largest value in an array, we determined the average number of executions of the assignment statement m k to be H n - 1. This, on its own, doesn’t give us a lot of information about the behavior of the algorithm. We need some more information. So we now ask the question, how close to the mean are the actual values that I have? 1.1 The difference One way to measure the “averageness” is to calculate the expected value of the deviation, that is, the average value of x - a , where x
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