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

$6$ , $6$ , $8$ , $8$ , $8$ , $10$ , $21$

Which of the following lists represents a data set that has the same median as the data set shown?

$4$ , $6$ , $6$ , $6$ , $8$ , $8$

$6$ , $6$ , $8$ , $8$ , $10$ , $10$

$6$ , $8$ , $10$ , $10$ , $10$ , $12$

$8$ , $8$ , $10$ , $10$ , $21$ , $21$

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Explanation

Choice B 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 data set shown has $7$ data values and is in ascending order, it follows that the median is the fourth data value in the list, or $8$ . If a data set contains an even number of data values, the median is between the two middle data values when the values are listed in ascending or descending order. Since each of the choices consists of a data set with $6$ data values in ascending order, it follows that the median is between the third and fourth data value. The third and fourth data values in choice B are $8$ and $8$ . Thus, choice B represents a data set with a median of $8$ . Since the median of the data set shown is $8$ and choice B represents a data set with a median of $8$ , it follows that choice B represents a data set that has the same median as the data set shown.

Choice A is incorrect. This list represents a data set with a median of $6$ , not $8$ .

Choice C is incorrect. This list represents a data set with a median of $10$ , not $8$ .

Choice D is incorrect. This list represents a data set with a median of $10$ , not $8$ .