A stem-and-leaf plot is a compact way to organize numerical data while keeping the original values visible. It shows the shape of a distribution, including clusters, gaps, skew, and outliers, without hiding individual data points. This makes it especially useful when a data set is small or medium sized and you still want exact values.
Students use stem-and-leaf plots to connect raw lists of numbers to more visual summaries like histograms and box plots.
To build one, split each value into a stem and a leaf, usually by place value. For example, in a data set of two-digit numbers, 47 can be written with stem 4 and leaf 7. The stems are listed in order, and the leaves are placed beside them in increasing order so the data become easy to scan.
A back-to-back stem-and-leaf plot uses one shared stem column to compare two related groups, such as test scores from two classes.
Key Facts
- In 47, using tens as stems, the stem is 4 and the leaf is 7.
- A key explains place value, such as 4 | 7 = 47.
- Leaves should be ordered from least to greatest within each stem.
- Number of leaves = number of data values, unless a split-stem design is used and values are still counted once.
- Range = maximum value - minimum value.
- A stem-and-leaf plot preserves exact data values, while a histogram groups values into intervals.
Vocabulary
- Stem
- The stem is the leading digit or group of digits that organizes data values by place value.
- Leaf
- The leaf is the final digit or digits attached to a stem to complete each data value.
- Key
- The key tells how to read the stems and leaves as actual numbers.
- Back-to-back stem-and-leaf plot
- A back-to-back stem-and-leaf plot compares two data sets using a shared stem column with leaves extending in opposite directions.
- Distribution
- A distribution describes how data values are spread across the number line, including center, spread, clusters, and outliers.
Common Mistakes to Avoid
- Forgetting the key is wrong because readers may not know whether 6 | 2 means 62, 6.2, or another value.
- Leaving leaves unordered is wrong because it makes the plot harder to read and can hide the median, clusters, and gaps.
- Mixing place values in one plot is wrong because stems and leaves must follow one consistent rule for every value.
- Treating repeated leaves as duplicates to remove is wrong because repeated values are real data points and must appear every time they occur.
Practice Questions
- 1 Create a stem-and-leaf plot for the data set 42, 37, 45, 41, 39, 52, 48, 44, 37, 50. Use tens digits as stems and ones digits as leaves.
- 2 The plot has key 6 | 3 = 63 and rows 4 | 8 9, 5 | 1 1 6, 6 | 0 3 7, 7 | 2. List the original data values, then find the range.
- 3 Two classes take the same quiz. Class A scores are tightly clustered around the 80s, while Class B has scores spread from the 50s to the 90s. Explain how a back-to-back stem-and-leaf plot would help compare the two classes better than two separate lists.