A tag named mean-value-theorem has been created quiterecently. (It is still listed among the new tags.) A tag with the same name was discussed before on meta and rejected: Tag proposal: mean-value-theorem.
However, looking at the questions where the tag-creator added this tag, it seems that the intention was to create a tag for the mean value property of harmonic functions rather than a tag for the mean value theorem from calculus. This raises quite naturally two questions:
- Should we have a separate tag for the mean value property?
- If yes, what should this tag be called?
In any case, using the name mean-value-theorem as the tag for mean value property might lead to confusion. (Most people will recognize result from introductory calculus under this name.) So even if a tag for mean value property is needed, I would suggest using a different name.
EDIT2: After the clarification from Guy Fsone that he intended the tag to include both harmonic/complex version and real analysis version, this older question might be related to this discussion as well: Do some calculus theorems deserve to have their own tag?