Which of the following statements demonstrates a negative correlation between two variables?
A.
People who play baseball more tend to have more hits
B.
Shorter people tend to weigh less than taller people
C.
Tennis balls that are older tend to have less bounce
D.
Cars that are older tend to have higher mileage
The Correct answer and Explanation is:
The correct answer is C. Tennis balls that are older tend to have less bounce.
Explanation
Correlation refers to a statistical relationship between two variables, indicating how one variable may change in relation to another. A negative correlation specifically implies that as one variable increases, the other variable tends to decrease. In this scenario, we are looking for a relationship where an increase in one aspect (the age of the tennis balls) results in a decrease in another aspect (the bounce of the tennis balls).
Option A states that people who play baseball more tend to have more hits. This describes a positive correlation; as participation in baseball increases, so do the hits.
Option B mentions that shorter people tend to weigh less than taller people. While this may suggest a general trend, it does not explicitly define a correlation. It suggests a possible negative relationship between height and weight but lacks clarity in the direction of the correlation.
Option D indicates that cars that are older tend to have higher mileage. This also suggests a positive correlation; older cars typically have been driven more, leading to higher mileage.
Option C effectively illustrates a negative correlation. As tennis balls age, they lose their elasticity and resilience, resulting in a decreased bounce. This relationship is clear: the older the tennis ball, the less bounce it exhibits, establishing a direct negative correlation between the age of the tennis balls and their performance in terms of bounce.
Understanding correlations is crucial in various fields, including psychology, economics, and sports science, as it helps in predicting behaviors and outcomes based on established relationships. Recognizing negative correlations allows for better decision-making, whether in product quality assessments or performance evaluations.