Final answer:
The most appropriate measure of center for data depends on its shape and whether it is symmetrically distributed, skewed or categorical.
Step-by-step explanation:
The question is asking about the appropriate measure of center based on the shape of the data. The measure of center refers to a value that represents the center or average of a dataset. In this case, the shape of the data should be examined to determine whether the mean, median, or mode is more appropriate.
If the data is symmetrically distributed, meaning it has a bell-shaped curve, the mean is the most appropriate measure of center. If the data is skewed or has outliers, the median is the most appropriate measure of center. If the data is categorical and the most frequently occurring value is of interest, then the mode is the most appropriate measure of center.
To determine which part of the question gives a more appropriate result for the data, it depends on the shape of the data. If the data is symmetrically distributed, part a may give a more appropriate result as it asks for the mean. If the data is skewed or has outliers, part c may give a more appropriate result as it asks for the median.