Question 1170317: An architect wants to determine the relationship between the heights (in feet) of a building and the number of stories in the building. The data for a sample of 10 buildings are shown below. Explain the relationship.
Stories 64 54 40 31 45 38 42 41 37 40
Height 841 725 635 616 615 582 535 520 511 485
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! To explain the relationship between the height of a building and the number of stories, we can analyze the data and look for patterns. Here's how we can approach this:
**1. Visual Inspection and Intuition**
* Looking at the data, it seems like generally, as the number of stories increases, the height of the building also increases. This suggests a positive relationship.
**2. Organizing the Data**
It's helpful to organize the data in a table:
| Stories | Height (feet) |
| :---------: | :---------------: |
| 64 | 841 |
| 54 | 725 |
| 40 | 635 |
| 31 | 616 |
| 45 | 615 |
| 38 | 582 |
| 42 | 535 |
| 41 | 520 |
| 37 | 511 |
| 40 | 485 |
**3. Analyzing the Relationship**
* **Positive Trend:** As mentioned earlier, there's a general positive trend. Higher story counts tend to correspond to greater heights. However, the relationship isn't perfectly linear. For example, the buildings with 40 stories have heights of 635 and 485, showing some variation.
* **Not Perfectly Linear:** The height doesn't increase by a constant amount for each additional story. The difference in height between buildings with consecutive story counts varies.
* **Potential Outliers:** We might consider the building with 45 stories and a height of 615 as potentially not fitting the general trend as well.
**4. Describing the Relationship**
Based on the analysis, we can describe the relationship as:
* There is a **positive correlation** between the number of stories in a building and its height. This means that taller buildings generally have more stories.
* The relationship is **not perfectly linear**. The increase in height per story is not constant. There's some variability in the data.
* Other factors besides the number of stories likely influence a building's height, such as ceiling height, architectural design, and zoning regulations.
**In summary:** The data indicates a general tendency for taller buildings to have more stories, but the relationship is not a precise one-to-one correspondence.
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