Final answer:
The standard deviation is the most appropriate measure to calculate when describing the amount of variability in a symmetric data set.
Step-by-step explanation:
If the goal is to describe the amount of variability in a symmetric data set, the most appropriate measure to calculate is the standard deviation. This statistical measure quantifies the amount of variation or dispersion in a data set. The standard deviation indicates how data points in a set deviate from the data set's mean. In other words, it measures how spread out the numbers are in your data set.
When the data set is symmetric, as stated in the question, the mean and median will be very close to each other, and a histogram or box plot will show this symmetry. The standard deviation is particularly useful in these scenarios as it helps explain the spread of the data around the mean. Symmetric distributions often follow what's known as the Empirical Rule: approximately 68 percent of the data is within one standard deviation of the mean, 95 percent is within two standard deviations, and over 99 percent is within three standard deviations.
This measure is very powerful because it allows us to understand the variability in the context of a symmetric distribution, enabling us to make statistical inferences about the data set such as the proportion of data within certain intervals around the mean. Hence, when working with symmetrical data, calculating the standard deviation is typically the recommended approach to assess variability.