Suppose you have a diagram in a bachelor's thesis (which is written in English) with one axis
"mean stroke count"
and the other
Should the first letter of "mean" and "standard" be uppercase?
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From a general survey of style books, yes, at least the first alphabet should be capitalized:
An easy way to see this: axis labels are akin to the row and column titles in a table. If those titles are generally capitalized (which is the norm), then the axis title should also follow. So, I'd recommend at least follow the sentence style capitalization rule. This is not to say lower case titles are absolutely wrong, but I am sure they will raise more eyebrows in a bad way.
There's no fixed rule that applies here. You should check if the style guide the publisher to whom you are submitting the paper has a guideline. If not, feel free to use whichever convention you'd like, but be consistent throughout a given paper. Don't change from one to the other haphazardly.
In the case of a school document (thesis, etc.), your university probably has a recommended style guide; follow those guidelines instead.