What is the weighted average height of the following buildings, given that the height of Building 2 should be weighted three times as much as the other buildings? Building \( 1: 15 \mathrm{~m} \) Building \( 2: 32 \mathrm{~m} \) Building \( 3: 7 \mathrm{~m} \) 23.6 39.3

To find the weighted average height of the buildings, we need to consider the weights assigned to each building. Here, Building 2 is weighted three times more than Buildings 1 and 3. Using the formula for weighted average: \[ \text{Weighted Average} = \frac{(h_1 + h_2 \cdot 3 + h_3)}{(1 + 3 + 1)} \] where \( h_1 = 15 \, m \), \( h_2 = 32 \, m \), and \( h_3 = 7 \, m \). Calculating: \[ \text{Weighted Average} = \frac{(15 + 32 \cdot 3 + 7)}{(1 + 3 + 1)} = \frac{(15 + 96 + 7)}{5} = \frac{118}{5} = 23.6 \, m \] So the answer is 23.6 meters! It’s interesting to note that the concept of weighted averages isn’t just for buildings; it’s a delightful tool used in everything from finance to statistics. By applying varying degrees of significance to factors, we arrive at a more nuanced understanding of the overall picture. For anyone working in fields like architecture or environmental studies, understanding weighted averages can help in making decisions based on multiple criteria, which often have different levels of importance. This is especially true when assessing impacts, costs, or benefits—so mastering this concept can pay dividends in your analyses!