Rationale
Mean is most affected by the perfect score of 100.
The mean, or average, is calculated by summing all scores and dividing by the number of scores. As the perfect score of 100 is significantly higher than the other scores within the 70-80 range, it increases the overall sum dramatically, thereby raising the mean value more than it would affect the median, mode, or percentile rank.
A) Mean
The mean is directly influenced by every score in the dataset. In this case, the perfect score of 100 will substantially raise the total sum of all scores, resulting in a higher average compared to the majority of scores that fall between 70 and 80. Thus, the mean will reflect this outlier effectively, demonstrating the greatest sensitivity to the perfect score.
B) Median
The median represents the middle value in a sorted list of scores. With nine scores in the 70-80 range and one score of 100, the median will still be within the 70-80 range and will not be affected by the perfect score, as it is determined by the middle values rather than the extremes.
C) Mode
The mode is the score that appears most frequently in the dataset. Since the majority of students scored between 70 and 80, the mode remains in this range, regardless of the existence of the perfect score. The mode does not change due to the presence of an outlier.
D) Percentile rank
Percentile rank indicates the percentage of scores that fall below a specific score. While the perfect score may elevate the overall ranking of one student, it does not fundamentally alter how many students scored below other scores. Thus, it has minimal impact on percentile ranks.
Conclusion
The perfect score of 100 significantly influences the mean by increasing the average of all test scores, which is not the case for the median, mode, or percentile rank. Understanding how different statistical measures respond to outliers is crucial in accurately interpreting data, particularly in educational assessments.
