Of course inversions of these tropes can be found all over the place so to properly see if there's a skew you'd need to analyse a whole lot of media and see which is more frequent. I'm not about to embark on that project so the best I can give you is a description of how it feels to me.
In the end I don't think these sorts of stereotypes are too unbalanced, for every bad female stereotype you can find a bad male stereotype. I feel like the conversation shouldn't be about who has it worse and deserves compensation, it should be about how we decouple both good and bad stereotypes from gender or skin color or sexual orientation or what have you.
You need stereotypes to tell compelling stories, otherwise you'd have to explain every single character in-depth. This isn't a bad thing, but we need to be more careful about attaching stereotypes needlessly to real existing groups of humans.
If I were a script writer and it'd be up to me I'd probably just write the script with whichever stereotypes it needs, and then once the script is done flip some coins for the irrelevant character attributes such as gender or skin color or eye color. As far as I can tell those basically never matter for telling a story. Even in the case of it being historically inaccurate I wouldn't say it matters: you're already suspending your disbelief for a lot of stuff in the movies, the idea that e.g. a woman would be a commander in the first world war isn't a stretch big enough to break immersion.
I need to learn to write more coherently and start a blog I think.
For example, if I were to pick a few top candidates for nerd representation in media I might pick the IT Show or CSI or Mr Robot.
- The Disappointments Room: David. At one point, he says that he plays Xbox and takes naps while he watches his wife Dana work, when he's asked what he does for a living.
- The sopranos: Tony Soprano has a hard time getting his son A.J. to do any work whatsoever.
- Seinfeld: George
And to be fair, the trope does have inverted instances as well, but again it seems to me to be uncommon:
- Married with children: Peg Bundy in the later seasons, Al bundy isn't much better though
> I asked for the most notable movies and shows.
And I ask god for a golden leprechaun every night, but that doesn't mean I'll get one. As a show of good faith I've spent some time researching an answer to your question, but just because you've posed a question doesn't mean you're entitled to an answer fulfilling your criteria.
There I suspect that the kid/woman v. dad/authority conflicts, the smart & pluck being on the first side and the obtuseness on the latter, really depicted the script writers v. the management.
Or if that's too far back, television's The Honeymooners (1955-1956). Or the Flintstones for that matter.
Or Fibber McGee and Molly if 30s radio shows are your thing.
The bumbling male and the stalwart woman is a trope that is thousands of years old.
Complaining about it is new.