Stumble and stagger have to do with walking. You can use them when you talk about someone who trips or walks with difficultly. Stagger is especially used to describe someone who is drunk. He stumbled over the bushes. He staggered out of the bar. Mumble is used to describe speaking which is hard to understand. He mumbled so I couldn't understand his directions. Bumble is used to describe someone who is generally clumsy and awkward - a klutz. Inspector Clouseau was a bumbling policeman.

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