1E Using the right number of stems
Chapter 1 · pages 30–35 · 1188 words
Choosing how to split a value between stem and leaf is not automatic: sometimes one digit's worth of stem gives too few lines (values crammed together), while moving the split one digit further gives too many lines (values spread too thin). Section 1E works through several ways to adjust the number of stems to fit the batch.
The stretched stem-and-leaf doubles the number of lines per starting part: one line carries leaves 0-4 and the next carries leaves 5-9, with the "*" tag shown only on the line holding leaves 0 and 1. Applied to Mississippi county land areas (rounded to tens of square miles), this produces a much clearer picture than a single line per starting part would, and lets a few distinctive counties (like Hinds, or Bolivar and Yazoo) be labeled right on the display:
3*|8 (1)
4*|0121243121300214202 (19)
4.|597886556569 (12)
5*|142010 (6)
5.|977899958797 (12)The squeezed stem-and-leaf goes the other way, using five lines per starting part instead of one line per digit, tagged * (zero/one), t (two/three), f (four/five), s (six/seven), and . (eight/nine) — a scheme that works because English digit names pair up neatly in fives. A batch running from 118 up through 330 can then be laid out compactly:
1*|1 (1)
t|2333 (4)
f|445555 (6)
s|66677 (5)
.|88 (2)
2*|0000011 (7)A third technique, mixed leaves, is used when the aim is mainly to collect values rather than scrutinize their shape, and especially when a few values trail far from the bulk of the batch. Here the split between starting part and leaf can change partway through the display — typically at a multiple of ten — and every such change is marked both by a change in the number of asterisks and by a blank line. A value can be handled two ways: for looking at, only the first digit or two of a long leaf is kept (1345 becomes 1|3, meaning "somewhere in the 1300s"); for storage, the entire leaf is kept (1345 becomes 1|345). The looking-at form sacrifices exact recovery of the original number in exchange for a picture; the storage form sacrifices compactness in exchange for being able to reconstruct every original value exactly. Multi-digit leaves in the storage form are separated by commas so their length stays unambiguous, and this style is well suited to batches running from many small values up to a few very large ones — values often pile up on and just after each power of ten, sometimes called the "abnormal law of large numbers."
Mixed-leaf displays can also mix leaf lengths within one display and handle negative and positive values together, which requires both a "+0" stem and a "-0" stem so that small positive and small negative values are kept apart. In one worked example, one-digit leaves are used from -59 up through +59, while two-digit leaves take over from -60 downward and +60 upward, letting the whole batch fit into 16 lines rather than the 31 that a uniform digit-width would have required.
Exhibits and original pages (5)
