OG详解-OG2 数学2 Q26

Choice B is correct. The histograms shown have the same shape, but data set A contains values between 20  and 60  and data set B contains values between 10 and 50. Thus, the mean of data set A is greater than the mean of data set B. Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is the difference between the smallest possible mean of data set A and the greatest possible mean of data set B. In data set A, since there are 3  integers in the interval greater than or equal to  20  but less   than 30, 4  integers greater than or equal to  30  but less than  40,  7  integers  greater than or equal to  40  but less than 50, and 9 integers greater than or equal to 50 but less than  60, the smallest possible mean for data set A is (3·20)+(4·30)+(7·40)+(9·50)23​​. In data set B, since there are  3  integers greater than or equal to 10  but less than  20,  4  integers greater than or equal to  20  but less  than 30, 7  integers greater than or equal to 30 but less than  40, and  9  integers greater than or equal to  40  but less than  50, the largest possible mean for data set B is (3·19)+(4·29)+(7·39)+(9·49​)23​.  Therefore, the smallest possibl difference between the mean of data set A and the mean of data set B (3·20)+(4·30)+(7·40)+(9·50)23​−(3·19)+(4·29)+(7·39)+(9·49)23​​ , which is equivalent t(3·20)−(3·19)+(4·30)−(4·29)+(7·40​)−(7·39)+(9·50)−(9·49)23​. This expression can be  rewritten as   3(20−9)+4(30−29)+7(40−39)+9(50−49​)23​  , or 23​23​, which is equal to  1.Therefore, the smallest possible difference between the mean of data set A and the mean of data set B is 1.
Choice A is incorrect. This is the smallest possible difference between the ranges,not the means, of the datasets. Choice C is incorrect. This is the difference between the greatest possible mean, not the smallest possible mean, of data set A and the greatest possible mean of data set B. Choice D is incorrect. This is  the smallest possible difference between the sum of the values in data set A and the sum of the values in data set B, not the smallest possible difference between the means.