Question

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Explanation:

Analyze the trend between x and y

Looking at the data points in the table:

• \(x = 1.6, y = 39\)
• \(x = 1.9, y = 38\)
• \(x = 2.3, y = 42\)
• \(x = 3.4, y = 40\)
• \(x = 3.8, y = 41\)
• \(x = 4.2, y = 44\)
• \(x = 4.3, y = 42\)
• \(x = 4.6, y = 45\)
• \(x = 4.8, y = 44\)

As \(x\) increases from \(1.6\) to \(4.8\), \(y\) generally increases from around \(38\text{–}39\) to \(44\text{–}45\). This indicates a positive association: as \(x\) increases, \(y\) increases.

Analyze the presence of clusters

A cluster is a distinct group of data points that are grouped closely together, separated from other data points.
The \(x\)-values are relatively evenly distributed across the interval from \(1.6\) to \(4.8\) without any distinct, isolated groupings or large gaps. Thus, there is not a cluster in this dataset.

Select the correct statement

Combining the two findings:

• There is not a cluster.
• As \(x\) increases, \(y\) increases.

This matches the third option.

Answer:

• (A) There is a cluster, and as x decreases, y increases.
• (B) There is a cluster, and as x increases, y increases.
• (C) There is not a cluster, and as x increases, y increases. (Correct answer)
• (D) There is not a cluster, and as x decreases, y increases.