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Problem-Solving and Data Analysis / One-variable data: Distributions and measures of center and spread Difficulty: Easy

Day	1	2	3	4	5
High temperature (°F)	81	80	81	81	82

The high temperature, in degrees Fahrenheit (°F), in a certain city was recorded for each of 5 days. The data are shown below.

Over this 5-day period, which of the following is NOT equal to 81°F?

Median of the high temperatures

Mean of the high temperatures

Mode of the high temperatures

Range of the high temperatures

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Explanation

Choice D is correct. The range of a data set is the difference between the maximum and the minimum values in the set. The maximum value among the high temperatures in the table is 82°F and the minimum value is 80°F. Therefore, the range is 82°F – 80°F = 2°F.

Choice A is incorrect. The median of a data set is the middle value when the values in the set are ordered from least to greatest. Ordering the high temperatures this way gives the list 80, 81, 81, 81, 82. Therefore, the median high temperature is 81°F. Choice B is incorrect. The mean high temperature is $the fraction with numerator 81, plus 80, plus 81, plus 81, plus 82, and denominator 5, equals, the fraction 405 over 5, which equals 81$ . Choice C is incorrect. The mode is the value that occurs the greatest number of times. For the set of high temperatures shown, 81 is the value that occurs 3 times, and therefore, 81°F is the mode of the high temperatures.