Final answer:
In the gymnastic competition, the typical score for Kathleen's performance on the uneven parallel bars is best reflected by the mode, which is 8.9, as it was the score most frequently awarded by the judges.
Step-by-step explanation:
The student has received various scores from 8 judges in a gymnastic competition. The calculation of the mean, median, and mode provides different perspectives on what can be considered a typical score. In this case, the mean is 8.8, the median is 8.85, and the mode is 8.9 for Kathleen's performance.
In statistics, the mean is the average of all scores and can be influenced by extremely high or low values, median is the middle value that divides the set of numbers and is less affected by outliers, and mode is the most frequently occurring score. For Kathleen's scores, since the values are quite close together and there doesn't appear to be any outliers skewing the mean significantly, all three measures are relatively close but the mode being the highest indicates a slight right skew in the scores distribution.
Although the mean and median are usually good indicators of the typical score, in this scenario, where the scores are tightly grouped and the highest frequency score (mode) is also the highest score, the mode at 8.9 might be the best reflection of a typical score because it represents the score that was awarded most often.