# Stem-Leaf Display

I am reading an example, one that is concerned with the topic mentioned in the title of this thread.

The example problem is:

"The use of alcohol by college students is of great concern not only to those in the academic community but also, because of potential health and safety consequences, to society at large. The article “Health and Behavioral Consequences of Binge Drinking in College” (J. of the Amer. Med. Assoc.,1994: 1672–1677) reported on a comprehensive study of heavy drinking on campuses across the United States. A binge episode was defined as five or more drinks in a row for males and four or more for females. Figure 1.4 shows a stem-and-leaf display of 140 values of $x=~the~percentage~of~binge~drinkers$ of undergraduate students who are binge drinkers. (These values were not given in the cited article, but our display agrees with a picture of the data that did appear.)"

So, from my understanding, the first row corresponds to the percentage value $04\%$; the second row corresponds to $11.34567889\%$, and so on.

What confuses me is a few statements they make later on:

Suppose the observations had been listed in alphabetical order by school name, as

$16\%$ $33\%$ $64\%$ $37\%$ $31\%$...

Then placing these values on the display in this order would result in the stem 1 row having 6 as its first leaf, and the beginning of the stem 3 row would be

3 | 371..."

Where are they getting these extra digits? And how does 3 | 371 correspond to the third entry of this list? If I was to write the stem-leaf display of these few pieces of data, I would write:

1 | 6

3 | 3

6 | 4

3 | 7

3 | 1

Is the book wrong?

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Are there really campuses where 60 odd percent of undergrads are binge drinkers? – Eckhard Dec 19 '12 at 21:28

Each digit after the vertical bar represents one observation. So the second row represents ten observations:
11%, 13%, 14%, 15%, 16%, 17%, 18%, 18%, 18%, 19%.

When the observations are listed in the order given, we have a 33%, a 37%, and then a 31%. So the row beginning with 3 would be
3 | 371

Does that make sense?

Edit: I wouldn't worry about it too much. Stem and leaf plots were handy in the days when you had to plot everything by hand, but there's basically no reason to use them anymore. That we still teach them in intro statistics classes is kind of silly.

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The edit isn’t entirely correct: they’re still a handy quick-and-dirty display of small amounts of numerical data (e.g., scores on an exam). You might as well say that there’s basically no reason to learn pencil-and-paper multiplication. – Brian M. Scott Dec 20 '12 at 2:36

The book is right. You should read up on the definition of stem-and-leaf displays. Your first table, for example means, that there was one school with 04% binge drinkers, one with 11%, 12%, ..., 17%, three with with 18%, one with 19%, and so on.

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The only information my book provides on this topic is how to construct one. This is what they write: $1$.Select one or more leading digits for the stem values. The trailing digits become the leaves.$2$.List possible stem values in a vertical column.$3$.Record the leaf for each observation beside the corresponding stem value.$4$.Indicate the units for stems and leaves someplace in the display. This didn't seem particularly helpful. – Mack Dec 21 '12 at 18:45