What a stem-and-leaf plot is
A stem-and-leaf plot (also called a stemplot) is a way of displaying a small-to-medium set of numbers so that you can see the shape of the data and still recover every original value. Each number is split into two parts: the leaf is the final digit, and the stem is everything to the left of it. The stems are written in a column, and the leaves for each stem are listed to the right in increasing order. The result looks like a sideways histogram, except the bars are made of the actual digits instead of blank rectangles.
For example, the values 42, 44, and 47 all share the stem 4 and produce the row 4 | 2 4 7. Reading it back, you reattach each leaf to its stem to get 42, 44, and 47.
How each value is split
- Two-digit numbers (10–99): tens digit is the stem, units digit is the leaf. So 63 becomes stem 6, leaf 3.
- Three-digit numbers (100–999): the first two digits are the stem and the last digit is the leaf. So 128 becomes stem 12, leaf 8.
- One-digit numbers (0–9): the stem is 0 and the digit itself is the leaf. So 7 becomes stem 0, leaf 7.
The key rule is consistency: every value must be split at the same place value so the stems line up and the length of each row honestly reflects how many values fall in that interval.
Why it is useful
Unlike a bar chart or histogram, the stem-and-leaf plot loses no information — the raw data is still readable. In one glance you can see the overall shape (symmetric, skewed, or bimodal), spot gaps and clusters, find the minimum and maximum, and locate the median simply by counting inward from both ends. It is a favorite in introductory statistics because it is quick to draw by hand and doubles as a sorted list.
Reading center and spread from the plot
- Median: because the leaves are already sorted, the median is the middle value — count in from either end. With an even count, average the two middle values.
- Mode: the value (or values) that appear most often; a repeated leaf in the same row signals it.
- Range: maximum minus minimum, both read directly off the top and bottom rows.
- Shape: a long tail of leaves toward the larger stems indicates right skew; toward the smaller stems, left skew.