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Lecture 19

PHYS 242 Lecture 19: PHYS242_Lecture_19-21

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PHYS 242
Wolfgang Rau

59 ENPHPHYS 242 Fall 2014 L 19 Distribution, Average, Probability Before we continue to discuss the statistical approach to physical phenomena here is a little reminder about some of the basic tools. As an example we use the Midterm results from a few years back. Distribution The diagram in Figure 28 shows how many students reached a given percentage in the midterm. Theaxis shows the percentage, the axis shows the number of students. For 70 e.g. we find 8 students, but for 71 we find also 8 students. This does not mean however, that this bar represents 16 students (or even more, because we would find the same number for all values between 67.5 and 72.5 ). This bar represents exactly those 8 students that achieved more than67.5 but not more than 72.5 . The axis label is consequently of students (5 bin). Figure 28: Result of a midterm exam. The axis shows the percentage, the axis indicates the number of students reaching the respective percentage. Each bar in the histogram represents all students who have percentages between the lower edge and the upper edge of that bar (e.g. there are 8 students with percentages between 67.5 and 72.5). Total number of students Each bar represents a certain number of students given by the product of the height of the bar and the binwidth. We find e.g. for the 9 bar (70 ): 8students 5 5 8 students. Consequently we can find the total number of students by adding all the bars: (51) Average To find the average we have to add what each student achieved and then divide by the total number of students. In the diagram we find: the first bar represents 1s tudent who achieved 1 30 ; the second bar represents 4 students who achieved 2 35 ; etc. The average is then given by (52) Probability Often one is not interested in the absolute number but in the probability: When choosing a random student what is the probability W. Rau
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