Final answer:
The mode is the most appropriate measure of central tendency for nominal variables as it represents the most frequent category in the data set. For symmetrical distributions, the mean, median, and mode are similar, but the median is less influenced by outliers and hence a better measure for skewed data.
Step-by-step explanation:
When dealing with a nominal variable, which is a type of variable that represents categories without a natural order or ranking, the most appropriate measure of central tendency is the mode. The mode is the value that appears most frequently in a data set. Contrary to the mean or median, which are more appropriate for numerical data, the mode can be used for both numerical and categorical data. As such, for nominal data which doesn't have a numerical ordering, the mode is the best choice because it indicates the most common category within the dataset.
In the context of symmetrical distributions, the mean, median, and mode will be the same or very close to each other. However, when there are outliers or the data is skewed, these measures of central tendency can differ significantly. The mean is sensitive to extreme values, which can distort the representation of the 'center' of the data set. The median provides a better central tendency measure for skewed distributions since it is less affected by outliers.