NUMB3RS - Season 3 - "Killer Chat" - Stylometry

Why do stylometrists look at entire distributions (like box-and-whisker plots) instead of just comparing simple averages?

Imagine two authors: Author X writes sentences that are consistently 14 to 16 words long. Author Y alternates between very short 2-word sentences and long, sweeping 28-word sentences. Both authors have a mean sentence length of exactly 15 words!

If we only look at the average, we would think their styles are identical. By using box-and-whisker plots, we can visually map the spread, symmetry, and dispersion of the writing samples to catch these stylistic fingerprints.