
schäbig
shabby
In poor, worn-out condition, often because of age or lack of care. Usually refers to objects, clothing, or places.
Er trug einen alten, schäbigen Mantel.
He was wearing an old, shabby coat.
shabby / mean
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shabby
In poor, worn-out condition, often because of age or lack of care. Usually refers to objects, clothing, or places.
Er trug einen alten, schäbigen Mantel.
He was wearing an old, shabby coat.

mean
Mean, unfair, or dishonorable in behavior toward other people.
Es war schäbig von ihm, dich so vor allen Leuten zu kritisieren.
It was mean of him to criticize you like that in front of everyone.
The meaning of 'schäbig' depends on the context. If it refers to objects or places, it means 'worn-out' or 'run-down'. If it refers to people's behavior, it means 'mean' or 'unfair'.
Das Hotelzimmer war klein und schäbig.
The hotel room was small and shabby.
In the meaning 'worn-out', 'schäbig' is often used to describe the poor condition of clothing, buildings, or furniture.
Er wohnte in einer schäbigen Gegend am Stadtrand.
He lived in a shabby area on the outskirts of town.
When it is about character or actions, 'schäbig' describes morally low or unfair behavior. Typical combinations are 'eine schäbige Ausrede' (a shabby excuse) or 'jemanden schäbig behandeln' (to treat someone badly/meanly).
Das war eine schäbige Lüge, um sich selbst zu schützen.
That was a mean lie to protect himself.
To criticize someone's unfair behavior, the construction 'Es ist schäbig von [person in the dative], ... zu ...' (It is mean of [person] to ...) is often used.
Es war schäbig von ihr, dir nicht die Wahrheit zu sagen.
It was mean of her not to tell you the truth.
mean / common
Gemein and schäbig both express a negative judgment of behavior. Gemein generally describes a malicious, unfair, or hurtful action. Schäbig is especially appropriate when the behavior also seems dishonorable or petty.

Es war schäbig von Paul, den Erfolg seiner Kollegin als seinen eigenen auszugeben.
It was shabby of Paul to pass off his colleague’s success as his own.
Es war gemein von Paul, seine Kollegin vor allen absichtlich zu verletzen.
It was mean of Paul to deliberately hurt his colleague in front of everyone.