OG详解-OG3 数学2 Q20

The correct answer is 44. The mean of adata set is computed by dividing the sum of the values in the data set by the number of values in the data set. It’sgiven that  data set A consists of the heights of  75  buildings and has a mean of  32  meters. This can be represented by the equation  x​75​ = 32, where x represents the sum of the heights of the buildings, in meters, in data set A. Multiplying both sides of this equation by 75 yields x = 75 (32), or x = 2,400  meters. Therefore, the sum of the heights of the buildings in data set A is  2,400  meters. It’s also given that data set B consists of the heights of  50  buildings and has a mean of  62  meters. This can be represented by the equation y50​​= 62, where y represents the sum of the heights of the buildings, in meters, in data set B. Multiplying both sides of   this equation by  50 yields y = 50 (62), or y = 3,100  meters. Therefore, the sum of the heights of the buildings in data set B is 3,100 meters. Since it’sgiven that data set C consists of the heights of the 125  buildings from datasets A and B, it follows that the mean of data set C is the sum of the heights of the buildings, in meters, in datasets A and B divided by the number of buildings represented in datasets A and B, or 2,400+3,100125​​, which is equivalent to 44 meters. Therefore, the mean, in meters, of data set C is 44.