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army1987 comments on Less Wrong Polls in Comments - Less Wrong
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Considering that the average word length in English is about five letters, I suspect that'd be quite far from being uniformly distributed.
Average is irrelevant. What's relevant is the standard deviation.
Since standard deviation goes as the square root of the number of items being added, phrase length for any reasonably-sized phrase, so long as it wasn't a line of poetry, should be pretty evenly distributed.