Final answer:
The appropriateness of using mean, median, or mode as a measure of center depends on whether the data is numerical and the presence of outliers or skewness. The median is robust against outliers, while the mean is ideal for symmetric data without outliers. The mode is applicable for nominal data.
Step-by-step explanation:
Do the measures of center make sense? To examine the shape of data or that part, a or c, of this question gives a more appropriate result for this data, we must consider whether the data is nominal or numerical. For numerical data, all measures of center, which include the mean, median, and mode, can be useful depending on the data distribution. The mean provides an arithmetic average whereas the median is less influenced by extreme values or outliers. The mode indicates the most frequently occurring value and is particularly useful for nominal data.
In determining which measure of center is most appropriate, we should consider the presence of skewness or outliers in the data distribution. The median tends to be more robust against outliers and is the best central measure in such cases. The mean, on the other hand, is most beneficial for symmetric distributions without outliers. When data is perfectly symmetrical, the mean, median, and mode are all identical. However, if there is skewness or outliers, the mean will be affected most, potentially leading to a distorted view of the data's center.
If the data is nominal, only the mode is applicable, as the mean and median require numerical data for computation. For symmetrical distributions, the mode may differ from the mean and median if there are multiple modes or if the data does not have a clear single most frequent value. When looking at numerical data that is bimodal, both modes would be considered, suggesting that for some numerical data sets, the mode can indeed be informative.