Data set A consists of the heights of 75 objects and has a mean of 25 meters. Data set B

Question

Data set A consists of the heights of 75 objects and has a mean of 25 meters. Data set B consists of the heights of 50 objects and has a mean of 65 meters. Data set C consists of the heights of the 125 objects from data sets A and B. What is the mean, in meters, of data set C?

Accepted Answer

The correct answer is 41 . The mean of a data set is computed by dividing the sum of the values in the data set by the number of values in the data set. It&rsquo;s given that data set A consists of the heights of 75 objects and has a mean of 25 meters. This can be represented by the equation x 75 = 25 , where x represents the sum of the heights of the objects, in meters, in data set A. Multiplying both sides of this equation by 75 yields x = 75 25 , or x = 1,875 meters. Therefore, the sum of the heights of the objects in data set A is 1,875 meters. It&rsquo;s also given that data set B consists of the heights of 50 objects and has a mean of 65 meters. This can be represented by the equation y 50 = 65 , where y represents the sum of the heights of the objects, in meters, in data set B. Multiplying both sides of this equation by 50 yields y = 50 65 , or y = 3,250 meters. Therefore, the sum of the heights of the objects in data set B is 3,250 meters. Since it&rsquo;s given that data set C consists of the heights of the 125 objects from data sets A and B, it follows that the mean of data set C is the sum of the heights of the objects, in meters, in data sets A and B divided by the number of objects represented in data sets A and B, or 1,875 + 3,250 125 , which is equivalent to 41 meters. Therefore, the mean, in meters, of data set C is 41 .

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