Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of data set C?

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 Solution:

Formula used, Mean = $\frac{\text{Sum of Dataset of n items}}{n}$

Given  Mean of A = 32 m (for 75 buildings)

            Mean of B = 62 m (for 50 buildings)

And, Mean of C = $\frac{\text{Sum of Dataset of 75 items of A + Sum of Dataset of 50 items of B}}{75+50}$

So, Sum of Dataset of 75 items of A =  Mean of A*75 = 32*75 = 2400 m

      Sum of Dataset of 50 items of A =  Mean of A*50 =  62*50 = 3100 m

Mean of C =  $\frac{\text{Sum of Dataset of 75 items of A + Sum of Dataset of 50 items of B}}{75+50}$

                  =  $\frac{2400 m + 3100 m}{75+50}$

                  =  $\frac{5500 m}{125}$

                  =  44 m



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