Question

Use the table to create a scatterplot. Determine the type of association.

This table presents the x and y values required to create scatter plots and determine the type of association.
x
25 30 80 150 250 350 425 450 500
y
375 225 120 75 50 100 175 275 400

Answer 1

To create a scatterplot using the provided x and y values, we will plot the points given in the table. The coordinates based on your data are as follows:

- (25, 375)
- (30, 225)
- (80, 120)
- (150, 75)
- (250, 50)
- (350, 100)
- (425, 175)
- (450, 275)
- (500, 400)

Now let’s visualize how these points would appear on a scatterplot. Each point corresponds to an x-value plotted against its corresponding y-value.

**Steps to create a scatterplot:**

1. Draw a set of axes, with the horizontal axis representing x-values and the vertical axis representing y-values.
2. Mark the x-values from 0 to a number greater than the maximum x-value (in this case, 500).
3. Mark the y-values similarly, choosing a range that covers the maximum y-value (here, 400).
4. Plot each of the points based on the coordinates provided.

**Analysis of the Type of Association:**
To determine the type of association:

- **Positive Association**: As x increases, y also increases.
- **Negative Association**: As x increases, y decreases.
- **No Association**: There's no discernible trend in how y changes relative to x.

From the provided data points:

- For smaller x-values (25, 30, 80), the y-values are high (375, 225, 120).
- As x continues to increase (up to about 250), the y-values decrease significantly until they hit a low of 50.
- After x=250, there’s a slight increase in y-values (to 100, 175, 275, and finally 400), but the initial overall trend seems to be decreasing.

Overall, the relationship appears to begin with a strong negative association as x increases from 25 to around 250, before shifting to a more positive association at higher x-values. Thus, the overall type of association can be described as **inverted U-shaped (initially negative, then slightly positive)** as we move through the data points.

If you were plotting this graphically, you would see a downward trend that subsequently begins to climb again, illustrating this mixed association visually.