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| 7.2 Concepts If two fifth grade classes took the same mathematics test and one class had a mean of 72 and the other had a mean of 86, what can be concluded about the mean of the combined test scores for the two classes? Discuss the largest possible mean in this example and the smallest possible mean. Under what conditions will the mean of all these test scores be the same as the mean of 72 and 86? Give an example. 7.2 Teaching The 7th national mathematics assessment found that when given a choice about which statistic to use, students tended to select the mean over the median regardless of the distribution of data (Zawojewski and Shaughnessy, 2000). Results from the Seventh Mathematics, Assessment of NAEP, page 237Assume that you are teaching a middle school class and the method in the school text for finding the mean of two numbers is to add the two numbers and divide by 2. Suppose one of your students discovered the following method for finding the mean of two numbers and wanted to know if it would always work: subtract the smaller from the larger; divide the difference by 2; and add the result to the smaller number. Show by using diagrams that the text’s method and the student’s method both produce the same mean. Then use algebra to show that both of these methods are equivalent. 7.2 Concepts Students need to understand that the mean “evens out” or “balances” a set of data and that the median identifies the “middle” of the data set. They should compare the utility of the mean and median as measures of center for different sets of data. NCTM Standards 2000, page 251The mean, median, and mode are called measures of central tendency and are different ways to use a single or “typical” number to give general information about many numbers. Match each of these measures to the following situations so that the measure gives the most helpful information: (1) a home buyer wants to know the typical cost of homes in a community; (2) students in a fifth grade want to know the typical height of the students in the class; and (3) a store owner needs to know the typical shoe size being sold by her business. Justify your reasoning for each of your choices and give examples to show why the central measure you selected is more appropriate than the other two measures. |