1

Problem

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

2

Step

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) = 2400 meters

3

Step

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 = 3100 meters

4

Step

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

5

Step

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

6

Step

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 "meters") / (125 "buildings") = 44 "meters"\$

7

Solution

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

8

Sumup

Please summarize steps

Choices

9

Choice-A

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

Wrong 42

10

Choice-B

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

Correct 44

11

Choice-C

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

Wrong 49

12

Choice-D

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

Wrong 52

13

Answer

Option

B

14

Sumup

Please summarize choices