The data for the dot plot are as follows: 22: 5 dots 23: 4 dots 24: 3 dots 25: 2

Question

The dot plot represents the $15$ values in data set A. Data set B is created by adding $56$ 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?

Accepted Answer

Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are 15 values in the data set, the eighth value in data set A, 23 , is the median. The maximum value in data set A is 26 and the minimum value is 22 , so the range of data set A is 26 - 22 , or 4 . It&rsquo;s given that data set B is created by adding 56 to each of the values in data set A. Increasing each of the 15 values in data set A by 56 will also increase its median value by 56 making the median of data set B 79 . Increasing each value of data set A by 56 does not change the range, since the maximum value of data set B is 26 + 56 , or 82 , and the minimum value is 22 + 56 , or 78 , making the range of data set B 82 - 78 , or 4 . Therefore, 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. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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