Question

after a week at camp wild scout, beth tracked the number of patches each scout earned. patches earned at camp wild scout (image of a dot plot with number of patches on the x - axis from 0 to 10, and dots at 1, 2, 3, 4, 6) select all the statements that describe the distribution of the data. there is a gap from 2 to 3 patches. there is a cluster from 1 to 4 patches. the distribution is roughly symmetric.

Explanation:

1. Gap Check: A gap is a range with no data. From 2 to 3, there are data points (x's at 2 and 3), so "There is a gap from 2 to 3 patches" is incorrect (the initial check was wrong).
2. Cluster Check: A cluster is a group of data points close together. From 1 to 4, there are x's (1:1, 2:3, 3:4, 4:2), so this is a cluster.
3. Symmetry Check: Symmetric distribution has data balanced around a center. The data has a peak at 3, with points at 1,2,3,4,6. It's not symmetric (e.g., 6 is a single point, no mirror on left). Wait, re - evaluating: Let's count the number of x's: at 1:1, 2:3, 3:4, 4:2, 6:1. The left side (1 - 4) has 1 + 3+4 + 2=10, right side (5 - 10) has 0 (at 5) + 1 (at 6) + 0+0+0+0 = 1. Wait, maybe the initial thought was wrong. Wait, the correct analysis:

• Gap: From 2 to 3: there are data points at 2 and 3, so no gap. So the first statement is wrong.
• Cluster: From 1 to 4, there are multiple data points (1,2,3,4 have x's), so this is a cluster.
• Symmetry: The data is not symmetric. The peak is at 3, and there's a single point at 6, with nothing in between 4 - 6 except at 6. So the "roughly symmetric" is wrong. Wait, maybe the original problem's initial checks were incorrect. Let's re - examine the dot plot:
• Number of patches: 1 (1 x), 2 (3 x's), 3 (4 x's), 4 (2 x's), 6 (1 x).
• For the gap: Between 2 and 3, there are x's at 2 and 3, so no gap. So the first statement is false.
• For the cluster: From 1 to 4, there are 1 + 3+4 + 2 = 10 x's, which is a cluster (many data points in a small range).
• For symmetry: The data on the left of 3 (1,2) and right of 3 (4,6) - the count at 1 (1) vs 6 (1), 2 (3) vs 4 (2) - not symmetric. So the correct statements are: "There is a cluster from 1 to 4 patches."

Answer:

The correct statement is: "There is a cluster from 1 to 4 patches." (Note: The initial marked statements had errors. The "gap from 2 to 3" is wrong as there are data points at 2 and 3, and "roughly symmetric" is wrong as the data is not balanced around a center. Only the cluster statement is correct.)