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

Number of employees	Number of restaurants
$2$ $2$ to $7$ $7$	$2$ $2$
$8$ $8$ to $13$ $13$	$4$ $4$
$14$ to $19$	$2$
$20$ to $25$	$7$
$26$ to $31$	$2$

The table shown summarizes the number of employees at each of the $17$ restaurants in a town.

Which of the following could be the median number of employees for the restaurants in this town?

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Explanation

Choice D is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the numbers of employees are given as ranges of values rather than specific values, it's only possible to determine the range in which the median falls, rather than the exact median. Since there are $17$ restaurants included in the data set and the numbers of employees are listed in ascending order, it follows that the median number of employees will be represented by the ninth restaurant in the list. Since the first $2$ restaurants each have $2$ to $7$ employees, numbers of employees in the $2$ to $7$ range would be represented by the first and second restaurants in the list. The next $4$ restaurants each have $8$ to $13$ employees. Therefore, numbers of employees in the $8$ to $13$ range will be represented by the third through sixth restaurants in the list. The next $2$ restaurants each have $14$ to $19$ employees. Therefore, numbers of employees in the $14$ to $19$ range will be represented by the seventh and eighth restaurants in the list. Since the next $7$ restaurants each have $20$ to $25$ employees, numbers of employees in the $20$ to $25$ range will be represented by the ninth through fifteenth restaurants in the list. This means that the ninth restaurant in the list, which has the median number of employees for the restaurants in this town, has a number of employees in the $20$ to $25$ range. Of the given choices, the only number of employees in the $20$ to $25$ range is $21$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the position of the median in the list, not the value of the median.

Choice C is incorrect and may result from conceptual or calculation errors.