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Problem-Solving and Data Analysis Difficulty: Medium

Data set A has $15$ values and is represented by the dot plot shown. Data set B is created by adding $46$ to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.

The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.

The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.

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Explanation

Choice A is correct. The median is the middle value in a data set when the data are arranged in order from least to greatest. Since there are $15$ values in data set A, the median is the $8th$ value. The $8th$ value is $23$ , so the median of data set A is $23$ . The range is found by subtracting the minimum value in a data set from the maximum value. The minimum value in data set A is $22$ and the maximum value is $26$ . Therefore, the range of data set A is $26 minus 22$ , or $4$ . It’s given that data set B is created by adding $46$ to each of the values in data set A. Therefore, the $8th$ value in data set B is $23 plus 46$ , or $69$ , so the median of data set B is $69$ . The minimum value in data set B is $22 plus 46$ , or $68$ , and the maximum value is $26 plus 46$ , or $72$ . Therefore, the range of data set B is $72 minus 68$ , or $4$ . Since the median of data set A is $23$ , and the median of data set B is $69$ , the median of data set B is greater than the median of data set A. Since the ranges of data sets A and B are both $4$ , the range of data set B is equal to the range of data set A.

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

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

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