The dots are counties - the largest red one above LA is Kern county - Tulare county is the smaller red dot above it to the right
This is a clearer version of that map. The other two much smaller red dots above LA are Kings and Inyo counties - this map is based on 2016 presidential results, as Inyo went blue in 2020 (by only 14 votes though)
The word average is often used to mean mean, however it can be used less specifically - median is a type of average as well.
From Merriam-Webster definition of average:
1a) a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values
Also, things like testosterone levels in a population usually follow a normal distribution, where both mean and median are the same, so the distinction is often meaningless for practical purposes