Question

recognizing outliers in a table
the data set in the table forms a cluster and does not
include outliers.
which point, if added to the table, would be an outlier?

Explanation:

Step1: Analyze the range of x - values

The original x - values are \(0.5,1,1.5,1.5,2,2.25,2.75\). The range of x - values is from \(0.5\) to \(2.75\).

Step2: Analyze the range of y - values

The original y - values are \(41,35,37,36,35,30,31\). The range of y - values is approximately from \(30\) to \(41\).

Step3: Check each option

• For the point \((0.5,42)\): The x - value \(0.5\) is within the range of original x - values, and \(y = 42\) is only slightly larger than the maximum \(y = 41\) of the original data.
• For the point \((1.25,35)\): The x - value \(1.25\) is between \(1\) and \(1.5\) (within the range of original x - values), and \(y = 35\) is an existing \(y\) - value in the original data.
• For the point \((2.75,41)\): The x - value \(2.75\) is an existing \(x\) - value in the original data, and \(y = 41\) is an existing \(y\) - value in the original data.
• For the point \((3.25,28)\): The x - value \(3.25\) is outside the range of original x - values (original x - values are at most \(2.75\)), and the \(y\) - value \(28\) is near the lower - end of the \(y\) - value range but the x - value deviation is more significant.

Answer:

\((3.25,28)\)