Stem-and-Leaf Plot
Statistics & ProbabilityA 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 tens digit) and the leaf (the ones digit). It shows all individual values while grouping them.
Example
Scores $72$, $75$, $78$, $81$, $83$, $87$, $91$: Stem $7$ | Leaves $2$ $5$ $8$; Stem $8$ | Leaves $1$ $3$ $7$; Stem $9$ | Leaf $1$. You can read back the original values from the plot.
Key Insight
A stem-and-leaf plot is like a histogram you can read backwards to recover the original data. It shows shape and keeps every value.
Definition
A stem-and-leaf plot divides each data value into a stem (leading digit(s)) and a leaf (final digit). Leaves are listed in order on each stem's row. The plot preserves all original values and reveals the shape of the distribution simultaneously. A back-to-back stem-and-leaf plot compares two datasets.
Example
Times (in seconds): $23$, $25$, $27$, $28$, $31$, $34$, $38$, $42$. Stems: $2$ | $3$ $5$ $7$ $8$; $3$ | $1$ $4$ $8$; $4$ | $2$. The median is between the $4$th and $5$th values ($28$ and $31$): median $= 29.5$.
Key Insight
The stem-and-leaf plot is unique in combining the roles of a frequency display and a data table. It is most useful for datasets with $15$-$100$ values and two-digit numbers.
Definition
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. The back-to-back variant enables formal comparison of two distributions' shapes and medians.
Example
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
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. Its philosophy, letting the data speak, remains central to modern EDA.