DOC Trying to improve Group by split-apply-combine guide
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

[Group by - split-apply-combine.pdf](https://github.com/pandas-dev/pandas/files/10951101/Group.by.-.split-apply-combine.pdf)

My aim was to make it easier for the reader. I removed some grammar errors, and tried to cut the lenght of very long sentences. 

Also:

- Ln: 46 The word "apply" doesn't make sense to me. I think that it's an error - but I need a reviewer to confirm please.
- Ln: 78 Removed "pandas objects can be split on any of their axes" - I think this needs to be removed because group_by axis=1 was deprecated. But again, it needs to be checked.
- Ln: 102 Same, I thought "axis labels" was not correct because of my previous comment. 
- Ln: 272 I'm not sure what you mean. Is "tab" supposed to work on vscode? or on ipython? 
- Ln: 364 Trying to cut the long sentence.

I wrote that I was going to do this on PR #51704.

Thanks a lot @rhshadrach  and @topper-123 for reviewing this PR /preview Website preview of this PR available at: https://pandas.pydata.org/preview/51916/ Thanks @DeaMariaLeon! Owee, I'm MrMeeseeks, Look at me.

There seem to be a conflict, please backport manually. Here are approximate instructions:

1. Checkout backport branch and update it.

```
git checkout 2.0.x
git pull
```

2. Cherry pick the first parent branch of the this PR on top of the older branch:
```
git cherry-pick -x -m1 c73c1c8cc34fded44e4262596f0f82631628e8b1
```

3. You will likely have some merge/cherry-pick conflict here, fix them and commit:

```
git commit -am 'Backport PR #51916: DOC Trying to improve Group by split-apply-combine guide'
```

4. Push to a named branch:

```
git push YOURFORK 2.0.x:auto-backport-of-pr-51916-on-2.0.x
```

5. Create a PR against branch 2.0.x, I would have named this PR:

> "Backport PR #51916 on branch 2.0.x (DOC Trying to improve Group by split-apply-combine guide)"

And apply the correct labels and milestones.

Congratulations — you did some good work! Hopefully your backport PR will be tested by the continuous integration and merged soon!

Remember to remove the `Still Needs Manual Backport` label once the PR gets merged.

If these instructions are inaccurate, feel free to [suggest an improvement](https://github.com/MeeseeksBox/MeeseeksDev).
                 When I tagged this as 2.0, I was thinking it'd be fine to ship with the 2.0 release since it's just docs in the user guide. However, looking at the conflicts, I now realize that part of this update includes the `axis=1` deprecation which will only be in 2.1. So I think we should not backport this.

I've removed the tag, but pinging people to make sure this doesn't mess anything else up. cc @datapythonista @simonjayhawkins  Thanks for the ping. Sounds good to me, since no backport PR has been created/merged I think the original milestone shouldn't affect anything, all good.