Question

the point (4, 10) is in each scatterplot. in which one is it an outlier?

Explanation:

Identify the position of the point (4, 10) in each scatterplot

In all four scatterplots, the point \( (4, 10) \) is plotted. We locate \( x = 4 \) on the horizontal axis and \( y = 10 \) on the vertical axis to find this point.

Analyze the pattern of the remaining data points in each option

• First scatterplot: Most points lie in a horizontal band around \( y = 5 \). The point \( (4, 10) \) is far above this main cluster of data, making it a clear outlier.
• Second scatterplot: There are only four points total, widely dispersed, with \( (4, 10) \) being one of the main data points defining the downward trend.
• Third scatterplot: Most points lie in a high horizontal band around \( y = 9 \) or \( y = 10 \). The point \( (4, 10) \) is part of this main group.
• Fourth scatterplot: The points show a strong positive, nearly vertical trend where \( y \) increases rapidly as \( x \) goes from 0 to 3. The point \( (4, 10) \) lies directly along this steep upward trend line.

Determine which scatterplot shows (4, 10) as an outlier

An outlier is a data point that deviates significantly from the overall pattern of the rest of the data. In the first scatterplot, the overall pattern is a horizontal cluster around \( y = 5 \), and \( (4, 10) \) lies completely outside this pattern.

Answer:

• (A) The first scatterplot, where most points cluster horizontally around \(y = 5\) and the point \((4, 10)\) is isolated far above them. (Correct answer)
• (B) The second scatterplot, which contains widely dispersed points showing a downward trend.
• (C) The third scatterplot, where most points are clustered near the top around \(y = 9\) and \(y = 10\).
• (D) The fourth scatterplot, where the points follow a steep upward trend that includes \((4, 10)\).