Question

leah claims the data in the table contains a cluster. why is leahs statement true?

there is no obvious outlier.
the \\(y\\)-values are steadily increasing as the \\(x\\)-values are decreasing.
the data contains a group of closely occurring points.
leahs statement is not true.

Explanation:

Define a cluster in bivariate data

A cluster in a scatterplot or bivariate data set is a distinct group of data points that lie close together.

Analyze the given data points

The data points are:

• \((35, 439)\)
• \((35, 440)\)
• \((39, 417)\)
• \((44, 615)\)
• \((44, 409)\)
• \((48, 403)\)
• \((49, 404)\)

Six of these seven points have \(y\)-values clustered tightly between \(403\) and \(440\) for \(x\)-values between \(35\) and \(49\). This concentration of closely occurring points forms a cluster, while the point \((44, 615)\) lies far away as an outlier.

Evaluate the given options

• "There is no obvious outlier" is false because \((44, 615)\) is a clear outlier.
• "The \(y\)-values are steadily increasing as the \(x\)-values are decreasing" is false.
• "The data contains a group of closely occurring points" correctly defines why a cluster exists.
• "Leah's statement is not true" is incorrect because a cluster is indeed present.

Answer:

• There is no obvious outlier.
• The y-values are steadily increasing as the x-values are decreasing.
• The data contains a group of closely occurring points. (Correct answer)
• Leah's statement is not true.