What a stem leaf plot calculator does
A stem leaf plot calculator converts a list of quantitative values into a stem-and-leaf display. The display keeps every original number (unlike many grouped graphs) while making the distribution easy to see.
Basic idea: split each observation into a stem (leading digits) and a leaf (trailing digit at a chosen place value), then list the leaves in increasing order for each stem.
With tens as stems and ones as leaves, the reconstruction rule is: \[ \text{value} = 10\cdot(\text{stem}) + (\text{leaf}). \]
Example dataset (test scores)
Consider the following 20 scores (out of 100):
| Raw data (unsorted) |
|---|
| 72, 66, 58, 75, 61, 84, 71, 62, 79, 56, 67, 73, 80, 64, 61, 68, 54, 77, 81, 72 |
Step-by-step construction (tens as stems, ones as leaves)
Step 1: Choose the place value for stems and leaves
Use the tens digit as the stem and the ones digit as the leaf. This is the default choice for two-digit whole-number data.
Step 2: Split each value into (stem | leaf)
Examples: \(54 \rightarrow 5\mid 4\), \(72 \rightarrow 7\mid 2\), \(84 \rightarrow 8\mid 4\).
Step 3: List leaves for each stem and sort the leaves
Each stem forms a row; leaves are written in increasing order (ties repeated).
Key: \(7\mid 2\) represents \(72\).
| Stem | Leaves (sorted) |
|---|---|
| 5 | 4 6 8 |
| 6 | 1 1 2 4 6 7 8 |
| 7 | 1 2 2 3 5 7 9 |
| 8 | 0 1 4 |
Visualization: the stem-and-leaf display
How to read center, spread, and shape from the display
1) Center (median) from the ordered list implied by the plot
There are \(n=20\) observations, so the median is the average of the 10th and 11th values in sorted order. Reading upward through the stems, the 10th and 11th values are \(68\) and \(71\), so: \[ \text{median}=\frac{68+71}{2}=69.5. \]
2) Spread (range) from the smallest and largest values
The smallest value is \(54\) and the largest value is \(84\). The range is: \[ 84-54=30. \]
3) Shape and potential outliers
- The heaviest concentration is in the 60s and 70s stems, suggesting a unimodal distribution centered near the high 60s/low 70s.
- Values in the 50s and 80s appear less frequent, indicating thinner tails in this sample.
- Potential outliers are assessed by comparing extreme leaves to the main body; for formal outlier rules, quartiles and the interquartile range are commonly used.
Common calculator settings and edge cases
Choosing a different stem unit
If values have three digits or the data are tightly clustered, the stem can be the first two digits (hundreds/tens) and the leaf the last digit, or stems can be split into two rows per decade (0–4 and 5–9) to reduce crowding.
Decimals
For one-decimal-place data, a typical choice is stem = integer part and leaf = tenths. The reconstruction rule becomes: \[ \text{value} = (\text{stem}) + 0.1\cdot(\text{leaf}). \]
Negative values
Negative values can be handled by keeping the sign with the stem (for example, \(-2\mid 3\) representing \(-23\) when tens are stems) and still ordering leaves within each stem consistently.
A stem leaf plot calculator is most informative when the stem/leaf choice produces several stems and a manageable number of leaves per stem, while the key makes the place value unambiguous.