Final answer:
The mode of the numbers 75, 93, 89, 75, 84 is 75, as it appears most frequently in the set. For the larger list of exam scores, the mode is 72. The mean is the measure of central tendency most affected by skewing in a data set.
Step-by-step explanation:
The mode of a set of numbers is the number that appears most frequently. Looking at the series 75, 93, 89, 75, 84, we can see that the number 75 appears twice, while the rest of the numbers appear only once. Therefore, the mode of this series is 75.
If we also look at the statistics exam scores for 20 students provided as 50, 53, 59, 59, 63, 63, 72, 72, 72, 72, 72, 76, 78, 81, 83, 84, 84, 84, 90, 93, the mode is 72, since it is the number that occurs most often in that list.
If we are looking for patterns in the mean, median, and mode, we can see that in a symmetric data set, these measures of central tendency can be very close to each other or even identical. However, if the data are skewed, the mean will be affected the most and will reflect the skewing more than the median or mode.