TRY IT YOURSELF The floor areas \( \left(\right. \) in \( \mathrm{m}^{2} \) ) of 6 apartments in building \( A \) are \( 63,94,78,80,71 \) and 62. The floor areas (in \( \mathrm{m}^{2} \) ) of 5 apartments in building \( B \) are 93, 104, 75,88 and 83. Find the median floor area of (a) the apartments in building \( A \), (b) the apartments in building \( B \), (c) all the apartments in the two buildings.

To find the median floor area of the apartments in buildings \( A \) and \( B \), as well as the combined data from both buildings, we will follow these steps: ### (a) Median of apartments in building \( A \) 1. **List the floor areas in ascending order**: \[ 62, 63, 71, 78, 80, 94 \] 2. **Count the number of apartments**: There are 6 apartments in building \( A \) (an even number). 3. **Find the median**: The median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th values in the ordered list: \[ \text{Median} = \frac{71 + 78}{2} = \frac{149}{2} = 74.5 \] ### (b) Median of apartments in building \( B \) 1. **List the floor areas in ascending order**: \[ 75, 83, 88, 93, 104 \] 2. **Count the number of apartments**: There are 5 apartments in building \( B \) (an odd number). 3. **Find the median**: The median is the middle number. The middle number is the 3rd value in the ordered list: \[ \text{Median} = 88 \] ### (c) Median of all apartments in both buildings 1. **Combine the floor areas from both buildings and list them in ascending order**: \[ 62, 63, 71, 75, 78, 80, 83, 88, 94, 104 \] 2. **Count the total number of apartments**: There are \( 6 + 5 = 11 \) apartments (an odd number). 3. **Find the median**: The median is the middle number. The middle number is the 6th value in the ordered list: \[ \text{Median} = 80 \] ### Summary of Medians - (a) Median of apartments in building \( A \): **74.5 m²** - (b) Median of apartments in building \( B \): **88 m²** - (c) Median of all apartments in both buildings: **80 m²**