OpenCourseWare on critical thinking, logic, and creativity

The importance of spread

In many contexts, the mean or median of a set of data is quoted without any indication of the spread of the data. Sometimes this is not a problem; for example, the fact that Yugoslav soccer player Savo Milosevic has scored an average of one goal every two games since 1994 is enough to tell you that he is an impressive striker. However, in other situations, knowledge of the spread is important.

In the following examples, see if you can spot the flaw in the reasoning, which in each case concerns overlooking the spread of some quantity.

• The average June temperatures in Hong Kong and Tucson, Arizona are both about 28C. So you can expect similar temperatures in Hong Kong and Tucson in June. Answer
• The average household size is 3.6 people. So new housing should be built to accommodate 3 to 4 person households. Answer
• The mean weight of one-year-old boys is 22.5 pounds. So parents of a one-year-old boy weighing 20 pounds should be concerned about their child's development. Answer
• Two students take an IQ test. Student 1 scores 98, and student 2 scores 101. Since the mean IQ score is defined to be 100, student 1 is of below average intelligence, and student 2 is above average. Answer

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