The Stem and Leaf Plot Generator turns a numeric list into a stem-and-leaf display: stems on the left, sorted leaves on the right, with a key that states how to read each row. Paste values separated by commas, spaces or line breaks; the generator sorts within each stem and can split stems or build a back-to-back plot for two groups.
Unlike a histogram, the plot keeps every original digit visible. You see shape and the raw values at once, which is why intro stats courses still assign these by hand.
Generate a stem and leaf plot
A stem is the leading digit(s); a leaf is the trailing digit. For two-digit scores, the tens digit is the stem and the units digit is the leaf. Paste the data, confirm the count, and the generator groups leaves under each stem in ascending order.
Choose stem width before reading shape. Scores from 8 to 98 fit tens stems; measurements from 102 to 148 may need hundreds as stems and tens as leaves, or a truncated stem with a stated unit in the key. Wrong width either piles everything on two rows or scatters single leaves down a long empty ladder.
Choose stem width when values span different magnitudes (hundreds versus tens). Wrong width produces either one overloaded stem or a long empty ladder of stems.
Read the plot key
Every stem and leaf plot needs a key that states what one stem-leaf pair represents in real units. Without a key, the pair 2 pipe 4 could mean 24, 2.4 or 240 depending on stem width.
The generator prints the key above the display using the active width, and copy exports include that key so a pasted plot remains readable in a document.
Example key: 2 | 4 means 24. That tells the reader the stem is tens and the leaf is units. The generator prints the key above the plot using the active stem width. Copy exports include the key so a pasted plot remains readable outside the page.
Split stems for a compressed plot
When only a few stems appear, the shape looks flat even if the data has structure inside each ten. Split stems divide each stem into two rows: leaves 0 to 4 on the first row and leaves 5 to 9 on the second for unit leaves.
Use splitting when the unsplit plot has fewer than about five occupied stems; skip it when stems are already plentiful across the range.
A set clustered in the 20s and 30s might show only stems 2 and 3. Splitting yields four rows and reveals whether values favour the low or high end of each ten. Use splitting when the unsplit plot has fewer than about five occupied stems; skip it when stems are already plentiful.
Build a back-to-back plot to compare two sets
A back-to-back plot shares one stem column. Leaves for group A grow left; leaves for group B grow right. Both sides sort outward from the stem. Keep both groups on the same stem width and the same leaf unit. Comparing a centimetre list with a millimetre list on shared stems without rescaling produces a meaningless picture.
When sample sizes differ a lot, compare shapes and centres rather than raw leaf counts alone.
Use it to compare two classes, two shifts or before/after measurements on the same scale. Shared stems keep the comparison fair; mismatched stem widths would distort the picture. The generator accepts two paste fields and aligns stems that appear in either set.
Create a plot for 12, 15, 15, 18, 22, 24, 31
Stems are tens digits and leaves are units on this list, with key 1 pipe 2 means 12. Four values fall in the teens, two in the twenties and one in the thirties. Leaves under each stem sort ascending, and the duplicate 15s appear as two leaf 5s under stem 1 rather than collapsing into a single count mark.
1 | 2 5 5 8
2 | 2 4
3 | 1Reading: four values in the teens (12, 15, 15, 18), two in the twenties (22, 24), one in the thirties (31). Leaves under stem 1 are sorted 2, 5, 5, 8. The repeated leaf 5 records the duplicate 15s; nothing is collapsed.
Read the shape of a distribution from the plot
Scan leaf counts down the stems. A symmetric mound peaks in the middle stems. A right skew shows a long run of stems toward higher values with sparse leaves. Gaps are empty stems between occupied ones. Clusters are stems with many leaves beside thinner neighbours.
Gaps matter as much as peaks. An empty stem between two occupied stems marks a hole in the observed values. Clusters of long leaf rows beside short neighbours mark local modes. On homework-sized lists those features are fragile, so describe them cautiously unless n is larger.
On the worked plot, mass sits in the teens with a thinner tail through the twenties into 31: a mild right lean, matching mean above median on the same numbers in the Descriptive Statistics Calculator. Shape calls from seven points are tentative; the same habits scale cleanly when n is larger.
Stem and leaf versus histogram
A histogram bins counts and discards which exact values fell inside each bin. A stem and leaf plot keeps every trailing digit, so the original list can be rebuilt from the display. That property makes these plots useful for short coursework data sets where the instructor still wants shape without losing the numbers.
Histograms scale better past a few hundred points, where a stem and leaf plot becomes a wall of digits. For large n, build a histogram in the Descriptive Statistics Calculator and keep stem and leaf for the compact classroom examples this page targets.
Building plots by hand for exams
Exams often forbid interactive tools, so the same algorithm should be muscle memory. Sort the data, decide the stem unit, write stems in a vertical column, then place each leaf in its row and sort leaves within the row. Add the key last, using one concrete pair from the data.
Graders mark missing keys heavily because an unmarked plot is ambiguous.
Back-to-back plots on exams usually share a short stem list written once in the centre. Leaves grow left for the first sample and right for the second. Keep digit sizes consistent so row length remains a fair visual comparison. If one sample is much larger, note the counts in a caption rather than implying equal mass from equal-looking rows.
Choosing stem width with examples
Scores 64, 67, 71, 73, 78, 82 fit stems 6, 7 and 8 with unit leaves. Reaction times 0.42, 0.45, 0.51 seconds fit stems as tenths with hundredths as leaves if the key says 0 pipe 42 means 0.42. State the unit once in the key and keep it fixed for the whole plot, including any back-to-back companion sample.
Duplicate leaves are required whenever values repeat. Collapsing two 15s into one leaf would understate frequency and break reconstruction of the raw list from the plot.
Frequently asked questions
What is a stem and leaf plot?
A stem and leaf plot displays numeric data by splitting each value into a leading stem and a trailing leaf, with leaves sorted beside their stem. It preserves individual values while showing distribution shape.
How do I read the key?
The key states what one stem-leaf pair represents. If the key says 2 | 4 means 24, stem 2 and leaf 4 encode twenty-four.
When should I split stems?
Split when the unsplit plot has too few stems to show shape, often fewer than five occupied stems. Splitting 0-4 and 5-9 leaves adds resolution inside each ten.
What is a back-to-back plot?
Two data sets share stems; one set's leaves go left and the other's go right. It compares shapes and centres on the same scale. Shared stem width is mandatory; otherwise the comparison is distorted.
Do duplicate values appear twice?
Yes. Each observation gets a leaf. Two 15s produce two leaf 5s under stem 1.
Can I use decimals?
Yes, with an appropriate stem width (for example stem = units, leaf = tenths). State that choice in the key so 3 | 2 means 3.2, not 32.
Is this the same as a histogram?
Related, but not identical. A histogram bins counts and loses the individual digits. A stem and leaf plot keeps every leaf, so the raw list can be rebuilt from the display.
Summary
The Stem and Leaf Plot Generator builds a labelled stem-and-leaf display from pasted numbers, with sorted leaves, a readable key, optional split stems and optional back-to-back comparison. Stems hold leading digits; leaves hold trailing digits; the key defines the place value.
Use the leaf pattern to spot skew, gaps and clusters while still seeing every value. Match stem width to the data's magnitude so the plot neither collapses into two rows nor stretches into a sparse ladder.