1H How far have we come? / 1K How to use stem-and-leaf to pick up additional information (optional technique)
Chapter 1 · pages 39–44 · 1110 words
This section closes the chapter with a summary, then adds an optional extra technique. The summary reminds us that every tool introduced so far — stem-and-leaf, tallying — exists to do one of two jobs: give a feeling for how a batch behaves as a whole, or store the values conveniently for later use. Sometimes, the author notes, you need one display for insight and a different one for storage, and there is no shame in making both. The chapter also names the whole enterprise: exploratory data analysis is "detective work," finding and revealing clues, while confirmatory data analysis (not covered in this book) goes further and assesses how strong the evidence is.
The summary also collects the practical lessons about stem-and-leaf itself: every display, however made, should at least be checked against the total count (overdotting makes this check easy for stem-and-leaf); leaves can be one digit, two digits, or mixed, chosen for convenience or necessity, and sometimes two styles are worth making side by side; and when you have many values and can sacrifice detail, tallying-by-tens is the efficient choice. The things a detailed display can reveal are named explicitly: separation, asymmetry, irregularities, centering, and width. The chapter then makes the case for why batches of similar numbers need special techniques at all — a single number like 46,930 motor-vehicle deaths, or a short table of death rates (trains 0.09, planes 0.16, buses 0.17, cars-turnpike 1.2, cars-general 2.3 per hundred million person-miles) can be grasped directly, but a whole batch of many similar numbers needs a display to be grasped "firmly or rapidly."
The optional section 1K then shows that stem-and-leaf's basic principle — the stem locates where you write, the leaf says more — can carry richer information than a single digit. Working from newspaper ads for 18 used-car sales, the model year becomes the stem and a coded letter or digit for the car's make becomes the leaf, so each entry is really a pair (year, make). Suggestive letters are used for makes where possible (F for Ford, C for Chevrolet), stepping out to digits only when letters run short, and capital versus small letters are kept distinct only where handwriting would naturally distinguish them (a book convention, not a rule of the technique). Organizing the leaves alphabetically within each stem year then exposes repeated name-year combinations at a glance — most strikingly, fifteen '65 Chevrolets show up as a run of identical leaves:
'63 | b B C C C F F I I I L O I C C b P
'64 | A B B C C C D D g h I I I M O P P r s 1 3 4
'65 | C C C C C C C C C C C C C C C
'66 | f t v h 1 C v 3 B 4 h F I v A C O h m P J F F C p 3Once you see leaves as carrying a code rather than just a digit, the same trick extends to storing pairs of numbers rather than a number and a category. The section illustrates this with 50 pairs — a logarithmic bank-deposit figure and a governor's salary — where the stem is the leading digits of the deposit figure and each leaf is itself a pair of numbers, such as stem 10 carrying leaves (4, 574) and (6, 556), which together decode to the full pairs (104, 574) and (106, 556). This shows that stem-and-leaf is not limited to single batches of plain numbers: the stem-plus-leaf idea generalizes to any situation where you want a compact, checkable way to store linked pieces of information.
Exhibits and original pages (5)
