1P Additional problems
Chapter 1 · pages 44–46 · 967 words
This closing section of Chapter 1 gives practice problems and then steps back to explain why the whole chapter's technique matters and what comes next. The three problems ask you to build stem-and-leaf displays from real scientific data — capillary-rheometer viscosity measurements, radial velocities of stars near Alpha Persei, and repeated measurements of a plutonium complex-ion association constant — and then to comment on the shape each display reveals. This is the same skill built up through 1C–1K: turn raw numbers into a stem-and-leaf picture, then read off its pattern.
The General comment that follows the problems reflects on the purpose of stem-and-leaf: it lets us scratch down a batch quickly and, more importantly, lets us see the batch's overall pattern. When a pattern is unusual — such as the three distinct groupings seen in Exhibit 10, or the asymmetric tailing-off seen in Exhibits 4 and 5, where the display stops more abruptly at the small end than the large end — we should describe that unusualness in words rather than expect any standard numerical summary to capture it.
This leads to the book's larger agenda: because we cannot expect a single "standard summary" to capture unusual features, future chapters will build a small set of agreed numbers — with agreed names, symbols, and standard ways of writing and plotting them — that summarize the typical characteristics of a batch's pattern. These summaries deliberately have limited ambition: they are meant to reveal what is more or less expected, not the exceptional. The chapter argues that summaries are useful and often necessary for large amounts of data, but they can never substitute for the full stem-and-leaf detail, which remains the tool for catching the unexpected.
The section closes with review questions asking why we summarize a batch at all, how completely we can expect summaries to succeed, how broad their aims can be, and how important full detail remains — questions that bridge directly into Chapter 2's topics of ranges, hinges, five-number summaries, and schematic plots, previewed here by the reproduced chapter index.
Exhibits and original pages (2)
