The standard deviation is a measure of "dispersion". But "dispersion" needs to have a focal point, and this focal point in the case of the standard deviation is the mean.
So "standard deviation is a measure of dispersion around the mean", of how "far on average" are the actual observations from their mean value.
The mean itself is a useful summary measure of the distribution of the data, if it represents indeed a focal point, a concentration point, a point around which the actual occurrences tend to cluster. But this implies that the mean is useful when the distribution is a) unimodal and b) has occurences "to the left and to the right" of its mode (maximum). Then the mean gives us roughly the value around which occurences hover.
But when the data is not roughly reminiscent of a "symmetric unimodal" shape (as is for Freshmen), but has the appearance of the distribution of Seniors, then the mean itself stops being really useful as a measure of concentration: evidently, Seniors occurrences do not hover around the sample mean.
But if the focal point around which and in relation to which the standard deviation is defined, is in itself not that useful as a metric and it does not summarize important aspects of the distribution that the data follow, then the standard deviation itself stops being also a useful measure.