The scatter plot below shows the relationship between the number of hours a student plays golf and the student’s class attendance. Which of the following types of correlation is shown on the scatter plot?

A.

Positive

B.

Positive and negative

C.

No correlation

D.

Negative

The Correct answer and Explanation is:

Correct Answer: D. Negative

Explanation:

In a scatter plot, the type of correlation between two variables is determined by the direction and pattern of the plotted data points. In this case, the relationship between the number of hours a student plays golf and the student’s class attendance is shown. To determine the correct type of correlation, let’s break down the key characteristics of each option:

1. Positive Correlation (Option A): A positive correlation occurs when both variables move in the same direction. As one variable increases, the other also increases, or as one decreases, the other decreases. For example, if the number of hours playing golf increased and the class attendance also increased, the data points would slope upwards from left to right. This is not what we expect here.
2. Positive and Negative Correlation (Option B): This option is incorrect because a scatter plot typically reflects only one type of relationship between two variables at a time—either positive or negative. A mixture of both correlations simultaneously would result in a complex or non-linear pattern, which is uncommon in a simple scatter plot analysis.
3. No Correlation (Option C): No correlation occurs when the data points are scattered randomly, with no discernible pattern. This would suggest that there is no relationship between the two variables, meaning changes in one variable do not consistently relate to changes in the other. In the context of the question, a scatter plot that shows no correlation would have data points that do not follow a clear upward or downward trend.
4. Negative Correlation (Option D): A negative correlation is when one variable increases while the other decreases. In this case, as the number of hours a student plays golf increases, class attendance decreases. The data points would slope downwards from left to right, indicating an inverse relationship. Given the context—students who spend more time playing golf likely have less time for attending classes—the scatter plot would show this downward trend, representing a negative correlation.

Thus, the correct answer is Negative Correlation (Option D). The scatter plot likely shows that as the hours spent playing golf increase, class attendance declines, illustrating an inverse relationship.