As a native speaker average is almost exclusively used to for mean and people specify median or mode when that’s what they are talking about. The same way people say mean without specifying arithmetic, geometric, or harmonic mean then it’s the arithmetic mean.

It’s only when someone says something like the average family rather than saying the average income when things get ambiguous. Typical on the other hand is closer to mean because it’s tossing out outliers.

I have to agree. Level of suck at management is also unrelated to any one quantified linear scale so the mean is the result of a particularly arbitrary personal (or national like GPA with range bias vs 0-20 with other bias) definition of a corresponding numerical ratings so median and mode have fewer degrees of freedom for arbitrary results.

It is also pretty absurd to assume without explanation that a minority who are especially bad at management have even their minority presence in management given that if sucking matters it should correlate with some type of failure that eventually correlates to drop out.