We don't have a normally distributed bell curve, in that incomes frequencies rise quickly, but then fall slowly, such that there's a "long tail."
http://theglitteringeye.com/images/us-income-distribution.gif
But we do have clustering of incomes near the median. For example, in 2020, median household income was $67,521. About 1/4 of household are between 75% of that and 125% of it, and about 3/4 of households earns between 50% and 200% of it. So, when we talk about medians, we're talking about something that is very close to about a quarter of the populations position, and fairly close to a large majority of the population's position.
As such, it's definitely not a meaningless measure. It's a good way of gauging roughly where the bulk of the society is sitting, which is helpful for addressing questions like whether the middle class has been gaining or losing ground.
There are other ways to look at it, though. See here:
https://www2.census.gov/programs-su...eries/historical-income-households/h01ar.xlsx
Using the "2020 Dollars" table there (so everything is adjusted for inflation, you can see how things have been going at the 20th, 40th, 60th, 80th, and 95th percentiles (where median just tells you where it has been for the 50th).
What you'll see if you look there is that each of those groups is up since 1982. If you take the 20th-40th percentile range as a proxy for the "working class" (not poor enough to be in the bottom tier, but not quite solidly middle class), then incomes rose from the range of $21,709-$41,288, 40 years ago, to the range of $27,026-$52,179 most recently. So, again, that's consistent with my view that they've generally gained ground.