Question the-da
- The data for the dot plot are as follows:
- 22: 5 dots
- 23: 4 dots
- 24: 3 dots
- 25: 2 dots
- 26: 1 dot
The dot plot represents the values in data set A. Data set B is created by adding 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 equal to 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 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 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 data for the dot plot are as follows: 22: 5 dots 23: 4 dots 24:
Hard-difficulty · SAT Math · One-Variable Data & Statistics — Effects of operations on data sets. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
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 values in the data set, the eighth value in data set A, , is the median. The maximum value in data set A is and the minimum value is , so the range of data set A is , or . It’s given that data set B is created by adding to each of the values in data set A. Increasing each of the values in data set A by will also increase its median value by making the median of data set B . Increasing each value of data set A by does not change the range, since the maximum value of data set B is , or , and the minimum value is , or , making the range of data set B , or . 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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