This thread gives more detail: Unexpected results from Summarize Within
It would be useful if the Summarize Within tool could give the option to summarise data that are not absolute/count data. For example, to be able to summarise travel times that have been created within ArcGIS Online, or data on mean income. The thread linked above gives a workaround that is straightforward for a user with a little experience, but frustrating to have to explain in a classroom setting. It seems that it is simple enough that it could be implemented behind the scenes so as to be transparent to the user.