Question

Graduation rate is one measure used to compare colleges in national publications. One such publication compared semester tuition against graduation rate, defined as the percentage of students who graduate within four years. The value of r for the scatterplot is 0.856.

A graph titled college comparisons has semester tuition (thousands of dollars) on the x-axis, and 4-year graduation rate (percentage) on the y-axis. Points are grouped together in a line with positive slope. Point (7, 80) is slightly outside of the other points.

Which statement best describes how the circled point influences the correlation shown in the scatterplot?

Because the point lies outside the linear trend, it weakens the correlation.
Because the point lies above the linear trend, it strengthens the correlation.
Because the point follows the linear trend, the correlation does not change.
Because the point lies outside the linear trend, it strengthens the correlation.

Answer 1

The statement that the point lies outside the linear trend, it weakens the correlation influences the correlation shown in the scatterplot. Hence the correct option is a.

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. A positive r value indicates a positive linear correlation, meaning that as one variable increases, the other tends to increase as well.

In this scenario, the scatterplot shows a positive linear trend with points grouped together in a line. The fact that point (7, 80) is slightly outside of the other points suggests that it deviates from the overall linear trend. When a point lies outside the general trend of the data, it can have a notable impact on the correlation coefficient. In this case, since the point (7, 80) is outside the linear trend and the correlation coefficient (r) is given as 0.856, the outlier weakens the correlation because it introduces variability that is not well captured by the linear relationship observed in the majority of the data points. Hence the correct option is a.