Stem-and-Leaf Plot
A stem-and-leaf plot organizes data by splitting each value into a stem (leading digits) and leaf (final digit), preserving the original data.
Definition
A stem-and-leaf plot organizes numbers by splitting each one into two parts: the stem (usually the leading digit(s)) and the leaf (the final digit), showing all individual values while grouping them. Leaves are listed in order on each stem's row, and the plot preserves all original values while revealing the shape of the distribution simultaneously; a back-to-back stem-and-leaf plot compares two datasets. Formally, a stem-and-leaf plot is a graphical display that preserves the exact data values while showing distributional shape, effectively providing a rotated histogram with unit-width bins; split stems (dividing each stem row into two) increase resolution, and the back-to-back variant enables formal comparison of two distributions' shapes and medians.
Example
For scores $72$, $75$, $78$, $81$, $83$, $87$, $91$: Stem $7$ | Leaves $2$ $5$ $8$; Stem $8$ | Leaves $1$ $3$ $7$; Stem $9$ | Leaf $1$, and you can read back the original values from the plot. For times (in seconds) $23$, $25$, $27$, $28$, $31$, $34$, $38$, $42$: Stems $2$ | $3$ $5$ $7$ $8$; $3$ | $1$ $4$ $8$; $4$ | $2$, with median between the $4$th and $5$th values ($28$ and $31$), so median $= 29.5$. For three-digit data (e.g., $142$, $157$, $163$), the stems are the first two digits and leaves are the units digit: $14$ | $2$; $15$ | $7$; $16$ | $3$; for data with four or more digits, rounding to three significant figures first is standard practice.
Key Insight
A stem-and-leaf plot is like a histogram you can read backwards to recover the original data, showing shape while keeping every value; it is most useful for datasets with $15$-$100$ values and two-digit numbers. Tukey's exploratory data analysis (EDA) framework introduced the stem-and-leaf plot as a computational tool for rapid summarization before the widespread availability of statistical software, and its philosophy, letting the data speak, remains central to modern EDA.