In a manner that is characteristic of or typical of an extrovert; in an outgoing or socially directed way.
From extrovertive (adjective) plus the adverbial suffix -ly, which comes from Old English -lice meaning 'like' or 'in the manner of.' This three-layer construction (extro- + -ive + -ly) shows how English builds increasingly specific modifiers.
English speakers use -ly to turn almost any adjective into an adverb, but it's remarkable that we can stack these meaning-layers so efficiently—compare 'extrovert' to 'extrovertively' and you've actually added two grammatical layers of meaning in just one syllable!
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