Question

identifying data sets that have outliers

which data sets (in graphic or table form) contain outliers? check all that apply.

Explanation:

Analyze the first scatterplot and second table

The first scatterplot shows points that lie perfectly along a straight line with a negative slope. There are no points deviating from this linear pattern, so it contains no outliers.

The first table has the following data points: \((60, -20)\), \((61, 0)\), \((63, 3)\), \((67, 8)\), and \((69, 8)\).
As \(x\) increases from \(61\) to \(69\), \(y\) increases gradually from \(0\) to \(8\). However, the point \((60, -20)\) has a \(y\)-value that is extremely far below the rest of the trend, making it a clear outlier.

Analyze the third scatterplot and fourth table

The second scatterplot shows a series of points following a decreasing curve or line, except for one point located significantly above the rest of the data trend at approximately \(x = 6\). This point is a clear outlier.

The second table has the following data points: \((1, 12)\), \((2, 21)\), \((3, 29)\), \((6, 51)\), and \((8, 70)\).
Calculating the rate of change between consecutive points:

• From \(x=1\) to \(x=2\): \(\Delta y / \Delta x = (21-12)/1 = 9\)
• From \(x=2\) to \(x=3\): \(\Delta y / \Delta x = (29-21)/1 = 8\)
• From \(x=3\) to \(x=6\): \(\Delta y / \Delta x = (51-29)/3 \approx 7.33\)
• From \(x=6\) to \(x=8\): \(\Delta y / \Delta x = (70-51)/2 = 9.5\)

All points follow a highly consistent, nearly linear positive relationship with a slope of approximately \(8\) to \(9\). There are no anomalous points deviating from this trend, so this data set contains no outliers.

Answer:

• (A) First scatterplot (linear downward trend with no deviating points)
• (B) Second data set (table with outlier at \((60, -20)\)) (Correct answer)
• (C) Third data set (scatterplot with one point plotted high above the downward trend) (Correct answer)
• (D) Fourth data set (table showing a consistent linear upward trend)