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 125 the buildings from data sets A and B.
What is the mean, in meters, of data set C?

Calculate the total height of buildings in data set A: \$"Total height from data set A" = ("Number of buildings in data set A") \times ("Mean height of data set A")\$

\$(75 "buildings") \times (32 "meters")/("building")\$ = 2400 meters

Calculate the total height of buildings in data set B: \$("Total height from data set B") = ("Number of buildings in data set B") \times ("Mean height of data set B")\$

\$(50 "buildings") \times (62 "meters")/("building")\$ = 3100 meters

Find the total combined height of data set C:
Total combined height of data set C = Total height from data set A + Total height from data set B
2400 meters + 3100 meters = 5500 meter.

Determine the total number of buildings in data set C :
Total number of buildings in data set C = Number of buildings in data set A + Number of buildings in data set B

75 buildings + 50 buildings = 125 building.

Calculate the mean height of data set C :
Mean height of data set C = \$("Total combined height of data set C")/("Total number of buildings in data set C")\$

\$(5500)/(125)\$ = 44 meters

So, the mean height of data set C is 44 meters.

This option is incorrect because it doesn’t match the calculation we made. The correct mean height for data set C is 44 meters, not 42 meters

42

This option is correct. We calculated the mean height of data set C to be 44 meters, which matches this option

44

This option suggests a mean height of 49 meters for data set C. However, this value does not match the calculations we performed

49

This option proposes that the mean height of data set C is 52 meters. Again, this value is not consistent with our calculations

52

Option

B

Can you summarize what you’ve understood in the above steps?