I’m not being pedantic, you’re just wrong. The average income in the US is deceptively high, whereas the median is quite low. This difference (or skew) is a sign of inequality.
The arithmetic mean, also called the average, or the expected value, is not the same type of calculation as the median.
There are many types of means or averages (harmonic, geometric, etc), but they all require a summation, an integral for continuous random variables and sigma notation for discrete. The median is the middle value. Totally different.
If someone checks “US average income” they’ll come away with the impression that Americans are rich.
If someone checks “US median income” they’ll come away with the impression that Americans are poor.
Median is not the same as average. Also, we don’t check math definitions in a dictionary, since we are not in middle school.