Question

a scatterplot is produced to compare the size of a school building to the number of students at that school who play an instrument. there are 12 data points, each representing a different school. the points are widely dispersed on the scatterplot without a pattern of grouping. which statement could be true?

there is no relationship between the size of a school building and the number of students who play an instrument because the scatterplot does not have a cluster.
as the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.
as the size of a school building increases, the number of student musicians decreases because the scatterplot has a cluster that decreases from left to right.
the size of a school building is equal to the number of students who play an instrument because the scatterplot does not have a cluster.

Explanation:

Analyze the given scatterplot description

The problem states that the points on the scatterplot are "widely dispersed... without a pattern of grouping." This means there is no visible trend, correlation, or cluster in the data.

Evaluate the options based on scatterplot properties

• Option 1: States there is no relationship because the scatterplot does not have a cluster. This matches the description of widely dispersed points without a pattern.
• Option 2: Claims an increasing relationship due to an increasing cluster, which contradicts the "no pattern of grouping" description.
• Option 3: Claims a decreasing relationship due to a decreasing cluster, which also contradicts the description.
• Option 4: Claims the two variables are equal, which is an incorrect interpretation of a lack of clusters.

Answer:

• (A) There is no relationship between the size of a school building and the number of students who play an instrument because the scatterplot does not have a cluster. (Correct answer)
• (B) As the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.
• (C) As the size of a school building increases, the number of student musicians decreases because the scatterplot has a cluster that decreases from left to right.
• (D) The size of a school building is equal to the number of students who play an instrument because the scatterplot does not have a cluster.