Which of the following relationships represents a negative correlation between two variables?
A.
As a student’s class attendance decreases, the student’s overall grade remains the same
B.
As the number of hours a person exercises decreases, the weight of that person remains unchanged
C.
As the number of miles driven increases, the amount of the gasoline in the tank decreases
D.
As the amount of water plant receives increases, the growth rate of the plant increase.
The correct answer and Explanation is :
The correct answer is:
C. As the number of miles driven increases, the amount of gasoline in the tank decreases
Explanation:
A negative correlation between two variables indicates that as one variable increases, the other variable tends to decrease, and vice versa. This means that there is an inverse relationship between the two variables.
Option C demonstrates a clear example of a negative correlation. In this case, as the number of miles driven increases, the amount of gasoline in the tank decreases. This is because driving more miles generally consumes more gasoline, thus reducing the amount left in the tank. This inverse relationship illustrates a negative correlation: as one variable (miles driven) increases, the other variable (amount of gasoline) decreases.
Let’s briefly analyze why the other options do not represent a negative correlation:
- Option A: As a student’s class attendance decreases, the student’s overall grade remains the same. This indicates that there is no correlation between class attendance and overall grade; the grade remains unchanged regardless of attendance. Hence, this does not represent a negative correlation.
- Option B: As the number of hours a person exercises decreases, the weight of that person remains unchanged. Similar to Option A, this shows no correlation between exercise hours and weight, as the weight does not change with varying exercise hours.
- Option D: As the amount of water a plant receives increases, the growth rate of the plant increases. This describes a positive correlation, not a negative one. In this scenario, both variables move in the same direction: as one increases, the other also increases.
In summary, Option C is the best representation of a negative correlation because it accurately reflects an inverse relationship between the number of miles driven and the amount of gasoline in the tank.