1. The table shows the distances, in meters, that each player in a game tossed a ball, and the total number of earned points each player made for those tosses.
Distance (m) 6.5 6 5 8.5 2 5.5 6.5 8 3 6 4.5 6
Total earned points 15 15 22 21 9 8 14 14 19 27 14 16

(a) Create a scatter plot of the data set. Use the distance for the input variable and the total earned points for the output variable.
(b) Are there any clusters or outliers in the data set? If so, identify them.

To create a scatter plot of the data set, we'll plot the distances on the x-axis (input variable) and the total earned points on the y-axis (output variable). Let's create the scatter plot:

(a) Scatter Plot:

```

Total Earned Points

^

30 +

|

25 +

|

20 + +

| +

15 + + + +

| + + +

10 + + +

| + + +

5 + +

+---------------------------------->

Distance (m)

```

(b) Analysis:

Looking at the scatter plot, we can observe a general positive correlation between distance and total earned points. As distance increases, the total earned points tend to increase as well.

Clusters:

- There appears to be a cluster of points around the lower end of the distance axis (around 2-6 meters) where total earned points vary.

- Another cluster seems to be around the middle range of distances (6-8.5 meters) where the total earned points are more consistent.

Outliers:

- There might be a potential outlier around 27 total earned points, corresponding to a distance of approximately 6 meters. This point is noticeably higher than the rest of the points in that distance range.

- Another potential outlier could be around 9 total earned points, corresponding to a distance of approximately 2 meters. This point is notably lower than the others in that distance range.