Final answer:
The mean is the appropriate measure of the true center in a symmetric data set, as it represents the average and balancing point of the data. It is calculated by summing all data values and dividing by the number of points.
Step-by-step explanation:
When the goal is to measure the true center, or balancing point, of a symmetric data set, the measure that should be calculated is the mean (average). The mean represents the sum of all the data values divided by the number of values in the data set. It is the most common measure of the center in statistics and provides the best estimate for the actual data set when the distribution is symmetric.
In a symmetric data set, the mean, median, and mode tend to coincide, reflecting the balance of the data around a central point. This is exemplified by a bell-shaped distribution, which is normal and symmetric where these three measures are the same. Since the mean is the arithmetic average, it can be easily calculated by adding up all the data values and then dividing by the number of data points.
In cases where the data set is not symmetric, particularly when there are outliers or extreme values, the median is often a better measure because it is not affected by these extreme values. However, given the data set is symmetric, as stated in the question, the mean is the most appropriate measure of the data's center.