An Unauthorized Biography of the Stem-And-Leaf Plot - Part II: A New Leaf

At the end of my previous post, aspiring statisticians Woodrow "Woody" Stem and August "Russell" Leaf, creators of the famed Stem-and-Leaf plot, were in bad shape. They had beaten each other statsless after an argument about the challenge given to them by their mentor, Dr. Histeaux Graham. That challenge: to devise a simple, yet elegant way to examine the distribution of values in a sample.

After their fateful bout of pugilism, Woody convalesced at the renowned Saint Tukey Center for Post Hoc Health. There, he continued to refine his theory of equally spaced intervals (or "bins," as he did eventually resort to calling them). His approach was great for evaluating the range of the sample—the proverbial minimum and maximum. But alas! How could he examine the values betwixt these values!?!  The problem vexed him greatly.

Russell sought care from the Gaussian order of the Brothers of Functional Likelihood. Their fabled monastery provided a quiet place for Russell to rest and think. And the brothers of the order also brewed a mean stout! (Their porter...meh. But the stout was absolutely to recover for!)  In the solitude and the dampitude of the large stone structure, Russell whiled away the days dipping his quill, creating random samples, sorting them, and meticulously copying the values onto artisanal parchment. (To this day, Russell's data sets are highly prized for their marginally ornate illustrations. [Or is that 'ornate margin illustrations'? I'm not sure. I'd have to look it up. So let's go with 'marginally ornate.'])

Russell bemused himself with art, he abused himself with stout, but he never disabused himself of one central notion: In order to understand a sample, one needed to know each value therein. Russell's methods did indeed gave him a deep understanding of each datum, but alas! How could he shine light on the nature of the distribution: the clumps, the gaps, the peaks, the tails, and, par chance, the outliers!?!  The problem vexed him greatly. Until that fateful day...

An Almighty Wind

It was a cloudy afternoon, sometime after both protagonists had regained the power of ambulation. Woody, still weak from his prolonged requiescence, sought the rejuvenation one can only derive from abundant fresh air. Strolling the local park, his head immersed in a dense cloud of smoke from his trusty briar, Woody chanced to glimpse a lone figure on a bench. The man appeared to be creating random samples, sorting them, and meticulously copying the values onto artisanal parchment. "What a dolt," Woody thought, and decided to go over and give the man a piece of his mind. And, in a way, that's just what he did.

Historians differ on exactly what happened next. Some say that as the two men—once friends, now bitter rivals—met each other's gaze, the clouds and smoke parted and a blinding shaft of light engulfed them both. (Mind you, this was before sunglasses.) The men froze, slack-jawed at the spectacle. A sudden gust wrested the pipe from Woody's weak fingers. The pipe flew up in the draft and struck first Woody, then Russell, thwacking each upside the head. It was as if God himself had grown weary of their stubbornness and had reached down from the heavens to give each of his beloved, but wayward children a dope slap. (I'm not sure what the other historians say about this event. I'd have to look it up, so let's go with dope slap.)

As the memory of their past friendship slowly returned to our heroes, each was suddenly able to look beyond his own foibles and prejudice to grasp the value-added synergies that might be realized from collaboration and cooperation, vis-à-vis cheating on their assignment. To this day, the creation that was inspired in that singular moment still bears the names of its creators.

(Some historians have also claimed that in the moment of epiphany, Woody's ever-present chocolate snack tumbled from his hand and came to rest in a bowl filled with a peanut-based butter substitute that Russell was known to enjoy. The result was said to have been quite tasty. However, these claims have never been substantiated.)

Amazing as this story is, some today have never heard of the Stem-and-Leaf plot. You see, Dr. Graham eventually appropriated (read 'stole') the ideas of his charges and created his own graph which he named after himself: Dr. Histeaux Graham's Magic Distribution Tonic. The name was later shortened to Histeaux Graham's Plot, and finally Histogram. (It was also known for a time by other names, such as Histeaux's Odyssey, the Graham Tracker, and That One With The Bars.)

Example of Dr. Graham's Tracker Plot (a.k.a. Histogram)

Eventually, with the advent of plotting machines, computers, and later the interwebs, the venerable Stem-and-Leaf plot fell into widespread disuse. It's just too easy these days to create a histogram. And many practitioners feel the histogram connotes a more sophisticated esthetic than does the cruder, but way-easier-to-make-by-hand Stem-and-Leaf plot.

But don't feel too bad for Dr. Stem and Dr. Leaf, gentle readers. For at least their crowning achievement is still known and revered, if only in statistical circles.

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