19. A class of ten students takes an exam on which nine of the students earn scores in the range of 70-80. One student earns a perfect score of 100. In examining the test scores, the professor notices that the perfect score has the largest effect on which of the following measures?
Answer: A
The perfect score has the largest effect on the mean.
The mean is significantly influenced by extreme values, such as the perfect score of 100 in this scenario. Since the majority of the students scored between 70-80, the inclusion of a perfect score raises the overall average score of the class.
A) Mean
This option is correct because the mean is calculated by summing all the scores and dividing by the number of scores. The perfect score of 100 increases the total sum considerably, thereby raising the mean more than any other measure would be affected.
B) Median
The median represents the middle score when all scores are arranged in order. In this case, since most scores fall between 70-80, the median is likely to remain within this range. The perfect score does not affect the middle value significantly, making this option incorrect.
C) Mode
The mode is the score that appears most frequently. Given that nine students scored between 70-80, the mode would likely be one of those scores. The perfect score does not contribute to the frequency of any score and therefore does not affect the mode, making this option incorrect.
D) Percentile rank
Percentile rank indicates the relative standing of a score within a dataset. While the perfect score may place that student in a higher percentile, it does not fundamentally alter the percentile ranks of other students significantly. Thus, this option is incorrect.
Conclusion
The mean is the measure most affected by the perfect score due to its sensitivity to extreme values, whereas the median, mode, and percentile rank remain largely unchanged. Therefore, option A is the only correct choice, as it accurately reflects how the perfect score influences the overall class performance.