To determine which scatter plot best displays the data, we need to look at the principles of a good scatter plot: using a reasonable scale on both axes and placing the explanatory variable on the [tex]\(x\)[/tex]-axis.
Firstly, let's identify the explanatory variable and the response variable from the data provided.
- The explanatory variable (independent variable) is the average high temperature in degrees Celsius.
- The response variable (dependent variable) is the number of ice cream cones sold.
The data provided shows:
| Month | Cones Sold | Average High Temp. (°C) |
|-------|------------|-------------------------|
| Jan | 0 | 1.0 |
| Feb | 0 | 3.0 |
| Mar | 30 | 7.3 |
| Apr | 61 | 14.3 |
| May | 118 | 21.2 |
| Jun | 426 | 26.1 |
| Jul | 485 | 28.6 |
For the scatter plot to be best, it should:
1. Place the average high temperature (°C) on the [tex]\(x\)[/tex]-axis.
2. Place the number of cones sold on the [tex]\(y\)[/tex]-axis.
3. Use a scale that fits the data well, ensuring both the [tex]\(x\)[/tex]-axis and [tex]\(y\)[/tex]-axis capture the range of the data accurately.
Given the data:
- The [tex]\(x\)[/tex]-axis should range from slightly below the minimum temperature (1.0°C) to slightly above the maximum temperature (28.6°C).
- The [tex]\(y\)[/tex]-axis should range from slightly below the minimum cones sold (0) to slightly above the maximum cones sold (485).
Without seeing the actual graphs, we can't evaluate the exact scales they use, but based on the criteria above, we can deduce the best graph:
- Graph A: If it places temperature on the [tex]\(x\)[/tex]-axis and cones sold on the [tex]\(y\)[/tex]-axis and uses a fitting scale for both axes.
- Graph B: If it places temperature on the [tex]\(x\)[/tex]-axis and cones sold on the [tex]\(y\)[/tex]-axis but uses an inappropriate scale, it won't be suitable.
- Graph C: Similar to B, if it uses the wrong scales, it won't be suitable.
- Graph D: If it accurately reflects the distribution of data compliance with the principles above, it would be suitable.
Therefore, correctly identifying the best scatter plot relies on checking whether:
1. The [tex]\(x\)[/tex]-axis and [tex]\(y\)[/tex]-axis are correctly labeled.
2. The scales on both axes are reasonable and fit the data range.
Since we can't visually inspect the scatter plots, the best conclusions are:
- Choose the graph that correctly places temperature on the [tex]\(x\)[/tex]-axis and cones sold on the [tex]\(y\)[/tex]-axis.
- Ensure the scales on both axes reasonably cover the data range.
So, the answer is to select the graph that fulfills these conditions. This information will likely allow you to match the description to the actual graph options given.
