NO, it is not finished.
The anime finished before the manga:
Anime finished: February 08, 2013
Manga finished: September 09, 2013
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Anime - Base
Release date: July 06, 2012
Anime - Sequel
Release date: February 08, 2013
Joshiraku is a slice-of-life comedy that centers around five young women who are also rakugo performers.
The anime focuses on their casual conversations and witty banter as they discuss a wide range of topics, from the mundane to the absurd.
Each episode showcases their unique personalities and perspectives, offering a humorous and satirical commentary on everyday life and popular culture.
The girls often find themselves backstage or in various locations around Tokyo, using their comedic storytelling skills to entertain each other and the audience.
Essentially, it's a show about the amusing and often random things these rakugo girls talk about.