Final answer:
The median is the middle value in a data set when ordered from lowest to highest, and in a symmetrical distribution, the median is equal to both the mean and the mode, representing a perfectly balanced data set.
Step-by-step explanation:
The median is the number that represents the middle response when the data are arranged in order from lowest to highest. In other words, it splits the data set into two halves where half the values are the same number or smaller than the median, and half the values are the same number or larger. It is particularly useful as a measure of the center of the data, especially when a data set contains outliers or extreme values that could skew the mean.
In a symmetrical distribution, the mean, median, and mode are all typically equal, indicating a perfectly balanced data distribution. However, in skewed distributions, the mean is usually pulled towards the tail, so it might not be the best measure of central tendency in such cases. The mode, being the most frequently occurring value, doesn't provide information about the symmetry but can indicate the value that appears most often, which can be useful for categorical data.