EXAMPLE 5 College Tuition

Jeanna plans to attend college in her home state of Massachusetts. She looks up the annual tuition and fees for all 64 four-year colleges in Massachusetts (omitting art schools and other special colleges). The data for the 2014/2015 academic year are displayed in the histogram in Figure 5.7. Notice that there are three bars tied for the tallest bar, representing 12 colleges charging between $30,000 and $35,000, $40,000 and $45,000, and $45,000 and $50,000, respectively. As is often the case, we can’t call this irregular distribution either symmetric or skewed. It does show two separate clusters of colleges, 12 with tuition and fees less than $15,000 and the remaining 52 costing more than $20,000. More generally, clusters suggest that different types of individuals are mixed in a dataset. In fact, the histogram in Figure 5.7 distinguishes 12 state colleges in Massachusetts from 52 private colleges, which charge much more.

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