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25 The histogram summarizes data set A, which represents the number of points per player earned by 50 players of a game. A new player earns 18 points playing the game, and this number of points is added to data set A to create data set B with 51 values. Which of the following must be true? I. The median number of points per player for data set B is less than the median number of points per player for data set A. II. The mean number of points per player for data set B is less than the mean number of points per player for data set A.
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The mean of a data set is the sum of the values divided by the 18 number of values. It’s given that a new player earns points playing the game, and this number of points is added to data set A to create data set B with 51 values. The histogram shows that all the values in data set A are greater than 18 18 . Since the additional number of points, , is less than any of the values in the original data set, the mean number of points per player for data set B is less than the mean number of points per player for data set A. The median of a data set with 50 25th 26th values is between the and values when the values are listed in 51 26th ascending order. The median of a data set with values is the value when the values are listed in ascending order. Therefore, the median of data set B is the 26th 25th value in data set B, which is the value in data set A. The histogram 25th 26th 50 shows that the and values in data set A are both between and 60 25th 26th points. Therefore, the and values in data set A could be equal, in 25th 26th which case the median of data set A would be equal to both the and values in data set A. Then, the median number of points per player for data set A would be equal to the median number of points per player for data set B. Therefore, only statement II must be true. Choice A 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.
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