Having a college education could totally be an indicator for middle class even if most people didn’t have one.
If you're in the capital class, you're getting your income from the assets you own. If you're in the working class, you're getting your income from working.
I've heard multiple definitions for a middle class, eiher one that owns some capital in the form of rental apartments or stocks, or that the middle class has a decenr amount of discretionary income.
Personally I don't think the middle class is that useful of a term to make sense of the economy. I also have a feeling that people like the term middle class because it muddies the waters when it comes to understanding the relationship between capital and labor.
Middle class is a state of mind