M119L05-page9 - As a simplifying assumption we are assuming...

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(Lesson 5: Measures of Center; 3-2) 3.09 PART D: ESTIMATING THE MEAN FROM A FREQUENCY TABLE Example 3 Following state requirements, 28 math teachers take a statistics test. Their test scores in points are described by the following frequency table: Score Classes Frequency f () 50-59 2 60-69 4 70-79 7 80-89 10 90-99 5 Estimate the mean of the test scores. Solution to Example 3 We are faced with limited, “grainy” information about the data set. We will replace each score class with its class mark , the midpoint of the class. For example, the class mark for the “60-69” class will be: 60 + 69 2 = 64.5 points . We are “boiling down” the classes into their marks. Note : If the data values had been rounded down, as is the case with ages, then 65 points may be a more appropriate choice for the class mark.
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Unformatted text preview: As a simplifying assumption, we are assuming that all four students in the class received a score of 64.5 points on the test. More generally, we could also assume that the average of the four students’ scores is 64.5 points. (Either assumption will have the same impact on our estimate of the mean.) Either way, our estimate for the sum of the four students’ scores will be: 64.5 + 64.5 + 64.5 + 64.5 = 4 ( ) 64.5 ( ) = 258 points . In general, our estimated “class sum” (i.e., the sum of the scores within a class) is given by f ± x , where f is the class frequency and x is the class mark. We will then add these class sums to obtain our estimate for the sum of all of the scores, f ± x ² ....
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