Answer :
Final answer:
The mode of the frequency distribution for the class intervals is the 35-40 interval. For the provided statistics exam scores, the mode is 72. The choice between using the mode or the mean for planning community college capacities will depend on specific planning goals.
Explanation:
Finding the Mode:
To find the mode of the given frequency distribution, we identify the class interval with the highest frequency since the mode is the value or interval that occurs most frequently in a data set. The class intervals provided are 25-30, 30-35, 35-40, 40-45, 45-50, and 50-55, with corresponding frequencies of 25, 34, 50, 42, 38, and 14, respectively.
Looking at the frequencies, we see that the interval 35-40 has the highest frequency of 50. Therefore, the mode of this frequency distribution is the interval 35-40.
For the provided statistics exam scores, to find the mode, we look for the score that appears most frequently. The scores are:
50, 53, 59, 59, 63, 63, 72, 72, 72, 72, 72, 76, 78, 81, 83, 84, 84, 84, 90, 93. The score of 72 appears the most, five times in total, which makes it the mode of this data set. Thus, the mode is 72.
When comparing the usefulness of the mode or the mean for planning community college capacities, the mode can give an idea of the most common enrollment size, which could be valuable for setting standard classroom sizes and staffing needs. However, the mean could provide a better measure of overall capacity needs, often reflecting the average size of enrollments more accurately. The choice between mode and mean depends on the specific planning goals.
