Stemplot
Stemplot
Stem-and-Leaf Plot
A simple way to display the shape of a distribution.
See also
Worked Example
Problem: Create a stemplot for the following test scores: 43, 51, 55, 58, 62, 63, 67, 71, 74, 78, 82, 85.
Step 1: Identify the stems. The tens digits range from 4 to 8, so the stems are 4, 5, 6, 7, and 8.
Step 2: Separate each value into stem | leaf. For example, 43 has stem 4 and leaf 3; 67 has stem 6 and leaf 7.
Step 3: List each stem once on the left of a vertical line, then write the corresponding leaves in ascending order to its right.
Answer: The completed stemplot:
4 | 3
5 | 1 5 8
6 | 2 3 7
7 | 1 4 8
8 | 2 5
Each row shows all values sharing that tens digit. You can quickly see the data clusters in the 50s, 60s, and 70s.
Why It Matters
A stemplot preserves every individual data value while also showing the overall shape of the distribution, something a histogram cannot do. This makes it especially useful for small to moderate data sets (roughly 15–100 values) where you want to spot clusters, gaps, and outliers at a glance. It is a standard tool in introductory statistics courses and on the AP Statistics exam.
Common Mistakes
Mistake: Writing leaves in random order instead of sorted order.
Correction: Always arrange the leaves from smallest to largest within each stem row. An unsorted stemplot makes it difficult to read the distribution shape or find the median.
Related Terms
- Boxplot — Another display summarizing data distribution
- Box-and-Whisker Plot — Visual summary using quartiles and extremes
- Histogram — Groups data into bins like a stemplot
- Distribution — The overall pattern a stemplot reveals
- Median — Easily found from a sorted stemplot