Question 34

The perfect score has the largest effect on the mean.

In this scenario, the mean is significantly influenced by the perfect score of 100 because it is an average that takes all values into account. Since nine students scored in the 70-80 range and one scored 100, the mean will increase notably due to the high perfect score.

A) Mean

The mean is calculated by adding all the scores together and dividing by the number of scores. The perfect score of 100 will raise the overall average significantly compared to the other scores, which are clustered between 70 and 80. Therefore, the mean is highly sensitive to this high outlier, making it the measure most affected by the perfect score.

B) Median

The median, which represents the middle value of a dataset when arranged in order, is less affected by extreme scores. In this case, the median would still reflect the central tendency of the nine scores in the 70-80 range, remaining stable despite the presence of the perfect score. Thus, the median does not experience a significant change.

C) Mode

The mode is the value that appears most frequently in a dataset. Since most students scored within the 70-80 range, the mode will be one of those scores, regardless of the perfect score. As the mode is based on frequency rather than value, the perfect score does not influence it.

D) Percentile rank

Percentile rank indicates the relative standing of a score in a dataset. While the perfect score may elevate the percentile rank of that student, it does not have the same broad impact on the overall distribution of scores as the mean. Therefore, percentile rank is less affected compared to the mean.

Conclusion

The mean is the measure most affected by the perfect score of 100, as it directly incorporates all scores into its calculation and is sensitive to outliers. In contrast, the median, mode, and percentile rank are less influenced by a single extreme score, making option A the definitive correct answer.