Question

1. higher order thinking the table shows the number of painters and sculptors enrolled in seven art schools. jashar makes an incorrect scatter plot to represent the data.

enrollment
number of painters\tnumber of sculptors
30\t25
43\t33
47\t50
30\t47
11\t6
48\t58
20\t45
a. what error did jashar likely make?
he most likely swapped the axis around
b. explain the relationship between the number of painters and sculptors enrolled in the art schools.
c. reasoning jashar’s scatter plot shows two possible outliers. identify them and explain why they are outliers.
(11,6) is an outlier because the number of painters is lower than other data points
(48,58) is an outlier because the number of painters and sculptors are really high compared to other data points

Explanation:

Part a:

Step1: Analyze Data Pairing

The table has two columns: Number of Painters and Number of Sculptors. Jashar's scatter plot likely swapped the axes (used Number of Sculptors for y - axis and Number of Painters for x - axis, or vice versa) because the data points in the plot don't align with the table values when axes are in the expected order (x: Painters, y: Sculptors or x: Sculptors, y: Painters). For example, a data point like (11,6) in the table (Painters = 11, Sculptors = 6) would be misrepresented if axes are swapped.

Step2: Confirm Error Type

By comparing the table data (e.g., Painters: 30,43,47,30,11,48,20; Sculptors:25,33,50,47,6,58,45) with the scatter plot's axes (x: Number of Sculptors, y: Number of Painters or similar swap), we see the error is a swap of the axes (misassigning which variable is on x - axis and y - axis).

Step1: Plot Expected Relationship

First, we can create a scatter plot with x as Number of Painters and y as Number of Sculptors (or vice versa) using the table data: (30,25),(43,33),(47,50),(30,47),(11,6),(48,58),(20,45).

Step2: Analyze Trend

When we plot these points, we can see that as the number of painters increases, the number of sculptors also tends to increase (positive correlation). For example, when painters go from 11 to 48, sculptors go from 6 to 58. We can calculate the correlation or just observe the general upward trend.

Step1: Identify Outliers

First, we list the data points for (Painters, Sculptors): (30,25),(43,33),(47,50),(30,47),(11,6),(48,58),(20,45). To find outliers, we can look at points that are far from the general cluster.

• For the point (11,6): Painters = 11, Sculptors = 6. Most other points have Painters ≥ 20 and Sculptors ≥ 25. So (11,6) is an outlier because it has a much lower number of both painters and sculptors compared to other schools.
• For the point (48,58): Painters = 48, Sculptors = 58. Most other points with similar painter counts (e.g., 43,47) have sculptor counts like 33,50. 58 is much higher than the sculptor counts for similar painter numbers, so (48,58) is an outlier.

Step2: Explain Outliers

(11,6) is an outlier because it has a very low number of both painters (11) and sculptors (6) compared to the other art schools (where painters are mostly ≥ 20 and sculptors ≥ 25). (48,58) is an outlier because for an art school with 48 painters, 58 sculptors is much higher than the sculptor counts of other schools with similar painter counts (e.g., 43 painters have 33 sculptors, 47 painters have 50 sculptors; 58 is higher than 50).

Answer:

Jashar likely swapped the axes (mixed up which variable, number of painters or sculptors, is plotted on the x - axis and y - axis).

Part b: