What is the relationship between mean, median, and mode in a perfectly symmetrical distribution?

In a perfectly symmetrical distribution, the relationship between mean, median, and mode is such that they all have the same value. This characteristic arises because symmetry implies that the data is evenly balanced around a central point.

In this context, the mean (the average of all data points), the median (the middle value when data points are arranged in order), and the mode (the most frequently occurring value) will coincide at the center of the distribution. This central point signifies the peak of the distribution and is the location where the highest frequency of data points occurs.

In practical terms, when a distribution is perfectly symmetrical, any shift in the values on either side of the center does not affect the central tendency measures in a way that differentiates them from one another; they remain equal. This equality makes option B the correct explanation of the relationship among mean, median, and mode in a perfectly symmetrical distribution.