Difficulty: Easy

Average Score: 86%

What effect would removing the outlier have on the relationship between variable 1 and variable 2?

Diagram for question

Rationale

It would weaken the positive relationship.

Removing an outlier from a dataset typically reduces the influence of that extreme value on the overall correlation, thereby leading to a weakening of any existing positive relationship between the two variables. Outliers can skew the results and give a misleading impression of the strength of the relationship.

A (It would weaken the positive relationship) CORRECT

Removing an outlier that is contributing disproportionately to a positive correlation means that the remaining data points may show a less pronounced relationship. The positive association could diminish as the outlier often inflates the strength of the correlation, leading to a more accurate but weaker relationship among the remaining data.

B (It would strengthen the positive relationship) YOUR ANSWER

This option incorrectly assumes that the presence of an outlier always enhances the positive relationship. In reality, outliers can distort the correlation, and their removal often clarifies and weakens the apparent positive association rather than strengthening it.

C (It would strengthen the neutral relationship) YOUR ANSWER

A neutral relationship indicates no correlation between the variables. Removing an outlier cannot strengthen a neutral relationship because there is no existing correlation to enhance; it may, however, lead to a clearer understanding of the lack of relationship.

D (It would weaken the neutral relationship) YOUR ANSWER

This choice suggests that removing an outlier could somehow affect a neutral relationship, which is incorrect. A neutral relationship is characterized by no correlation, and the removal of an outlier does not change the inherent lack of association between the two variables.

Conclusion

Removing an outlier from a dataset generally weakens the positive relationship between two variables by reducing the skewing effect caused by the extreme value. This emphasizes the importance of understanding the impact of outliers on data analysis to arrive at more accurate interpretations of correlations.

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