Question

question #6
the coaches of a group of debate teams answered a survey about hours of debate, team practice, and number of team wins. the graph shows the results of this survey.

the scatterplot indicates which of the following?

as they practice more hours per week, the number of debates won decreases.
there is a dual correlation between the number of hours they practice each week and the number of debates they win.
as they practice more hours per week, the number of debates won increases.
there is no correlation between the number of hours practiced per week and the number of debates they win.

Explanation:

Step1: Analyze the scatter - plot trend

In a scatter - plot, if the points generally move from the lower left to the upper right, there is a positive correlation. If they move from the upper left to the lower right, there is a negative correlation.
Looking at the given scatter - plot of hours of practice per week (x - axis) and debates won (y - axis), we observe that as the value on the x - axis (hours of practice) increases, the value on the y - axis (debates won) first increases and then decreases.

Step2: Evaluate each option

• Option 1: “As they practice more hours per week, the number of debates won decreases.” This is incorrect because initially, as hours of practice increase, the number of debates won increases.
• Option 2: “There is a dual correlation between the number of hours they practice each week and the number of debates they win.” A dual (or non - linear) correlation is indicated when the relationship between two variables is not a simple straight - line (linear) relationship. In this scatter - plot, as hours of practice increase, the number of debates won first goes up and then goes down, which is a non - linear (dual) relationship.
• Option 3: “As they practice more hours per week, the number of debates won increases.” This is incorrect because after a certain number of practice hours, as practice hours increase, the number of debates won decreases.
• Option 4: “There is no correlation between the number of hours practiced per week and the number of debates they win.” This is incorrect because there is a clear pattern (first increasing then decreasing) in the relationship between hours of practice and debates won.

Answer:

There is a dual correlation between the number of hours they practice each week and the number of debates they win.