The mean is not necessarily the best single number to serve as an index of such a
change. The median is also a good index, and changes in the 25th percentile, the
percent above some minimal value, the standard deviation, or the interquartile range
could also be valid indicators of changes in the underlying educational process. As
long as a process remains stable, we expect the mean, or any of these other statistical
indices obtained from that process, to remain relatively unchanged from sample to
sample. Conversely, when a statistic from a large sample changes appreciably, we
assume that the process has changed in some way.