A stem-and-leaf plot splits every number into two parts. The leading digits become the stem, and the final digit becomes the leaf. Write each stem once down the left, list its leaves in order to the right, and you have a display that shows the shape of the distribution like a histogram while still preserving every individual observation. This calculator builds that display properly: leaves sorted, empty stems retained, a key printed underneath, and stems split automatically when the data is too clustered for one row per stem to be informative.
Arb Digital publishes free statistics tools that produce the output an assignment or a report actually asks for. The histogram calculator bins data into bars and discards the individual values; the box plot calculator reduces it to five numbers and some outliers. A stem-and-leaf plot sits between them: same shape information, nothing thrown away, and it can be drawn by hand — which is exactly why it is still taught.
What This Stem and Leaf Plot Calculator Does
It reads your data, works out a sensible leaf unit from the range, splits each value into a stem and a leaf, and lays the display out in a fixed-width grid so the leaf columns line up. Every stem between the smallest and the largest appears, including the empty ones, because a gap in the data is information and dropping the row hides it. Leaves are sorted within each row, which is what distinguishes an ordered stem-and-leaf plot from a rough sketch.
Alongside the display you get the number of values plotted, the number of rows, the leaf unit in force, and the median — which you can also read straight off the plot by counting leaves. The panel underneath states the key, the frequency for each row, and, when splitting is applied, why it was applied.
How to Use It
- Paste the data. Any separator works. Values are not required to be sorted; the tool sorts the leaves for you.
- Leave the leaf unit on auto unless your assignment specifies one. Auto picks the place value that gives a readable number of stems.
- Leave splitting on auto too. It only triggers when the number of stems is small relative to the number of values.
- Read the key before the plot. The same display means completely different things at a leaf unit of 1 and a leaf unit of 10.
- Count leaves to find positions. The median, quartiles and mode can all be read off the display directly, which is a large part of why it exists.
How the Split Is Made
With a leaf unit of 1, each value is divided by 10. The whole-number part is the stem and the remainder is the leaf, so 34 becomes stem 3, leaf 4, and 7 becomes stem 0, leaf 7. Change the leaf unit to 10 and every value is first divided by 10, so 340 becomes stem 3, leaf 4, and the key reads "3 | 4 = 340". Change it to 0.1 and 3.4 becomes stem 3, leaf 4 with the key reading "3 | 4 = 3.4". The digits on the page are identical in all three cases, which is why the key is not optional.
Work the default by hand. The fifteen values 23, 25, 27, 28, 31, 32, 34, 34, 36, 41, 43, 45, 52, 55, 67 give stems 2 through 6. Stem 2 collects leaves 3, 5, 7, 8; stem 3 collects 1, 2, 4, 4, 6; stem 4 collects 1, 3, 5; stem 5 collects 2, 5; and stem 6 collects a single 7. Row frequencies of 4, 5, 3, 2, 1 describe a distribution that peaks in the thirties and tails off to the right — visible immediately in the display, and confirmed numerically by the descriptive statistics calculator.
Split Stems, and Why Clustered Data Needs Them
Suppose forty exam marks all fall between 60 and 89. One row per stem gives you exactly three rows, each carrying twelve or more leaves. That is a display with no shape at all — three long strings tell you nothing about where inside the sixties the values sit. The standard fix is to split each stem into two rows, one holding leaves 0 to 4 and one holding leaves 5 to 9, which doubles the resolution without changing a single value.
For extremely tight data the same idea extends to five rows per stem, holding leaves 0-1, 2-3, 4-5, 6-7 and 8-9. Splitting into two or five is conventional because both divide ten evenly; splitting into three would put unequal numbers of possible leaves in each row and distort the apparent shape, which is precisely the mistake a histogram with unequal bins makes. This tool's auto mode splits when the number of stems is fewer than about five, or when the average row would carry more than eight leaves. The NIST/SEMATECH catalogue of graphical techniques covers the wider family of exploratory displays that this belongs to.
Truncating Versus Rounding the Leaf
When a value carries more digits than the stem and leaf can hold, something has to go. The textbook convention is to truncate, not round: with a leaf unit of 1, the value 34.7 is displayed as stem 3, leaf 4, not stem 3, leaf 5. This tool truncates, which is what most courses expect and what keeps the display consistent with the stated key.
The consequence is worth stating plainly. A stem-and-leaf plot of truncated data is a faithful picture of the shape but not a lossless record of the original numbers, so a median read off the plot can differ slightly from a median computed from the raw data. Where that matters, compute the statistic from the data rather than from the display — the mean, median and mode calculator and the five-number summary calculator both work from the raw values.
Reading Shape, Gaps and Clusters Off the Display
Turn the plot ninety degrees anticlockwise and it is a histogram, so everything you know about reading histogram shape applies. A long string of leaves at the bottom rows with short rows above means right skew. Two separated bulges with a sparse row between them means the data probably mixes two populations — different classes, different traffic sources, different machines — and no single average will describe either of them well.
The feature a histogram usually hides is the gap. Because empty stems are kept, a run of blank rows is visible as blank rows, whereas a histogram bin of width 10 would quietly absorb it. A gap followed by one isolated leaf is the classic signature of an outlier, and unlike a box plot, the display tells you the actual value rather than just marking a dot. Once you have spotted it, the outlier calculator will tell you whether it clears the conventional fence.
When a Stem and Leaf Plot Is the Wrong Choice
It has a working range. Below about fifteen values there is not enough data for the shape to mean anything, and above roughly one hundred and fifty the rows become unmanageably long and a histogram is simply easier to read. It also assumes your data sits comfortably in a decimal digit structure; values spanning several orders of magnitude, from 3 to 30,000, cannot be displayed sensibly at any single leaf unit.
Categorical data cannot be plotted this way at all, since there are no digits to split, and a frequency distribution or a bar chart is the right tool there. For comparing several groups, back-to-back displays work for two groups but not for five, where box plots win outright. Penn State's open STAT 200 elementary statistics course sets out where each display belongs in an exploratory workflow.
Arb Digital builds analytics reporting that shows the distribution behind the average, not just the average.
Browse All Free Tools Talk To Our TeamBack-to-Back Displays and Other Variants
Two groups can share one column of stems, with one group's leaves running left and the other's running right. That back-to-back arrangement is the most compact honest way to compare two distributions on paper, because both groups are measured against the same stems and no binning choice can favour one over the other. It works well up to about sixty values per side and falls apart beyond that, at which point paired box plots or overlaid density curves take over.
Two other variants appear in textbooks. A cumulative or "depth" column adds a running count in from each end towards the median, which makes reading the quartiles almost mechanical. And where the leaf digit carries no useful precision — heights recorded to the nearest centimetre in a population spanning a metre, say — some authors write leaves as pairs of digits with a comma between them. That is legitimate as long as the key says so explicitly, but it costs the display its main advantage of being readable at a glance, and a histogram is usually the better answer at that point.
Common Mistakes to Avoid
- Omitting the key — without it the same display could mean 34, 3.4 or 340.
- Dropping empty stems, which erases gaps in the data and distorts the apparent shape.
- Leaving the leaves unsorted, which makes the display much harder to read and is marked down in most courses.
- Rounding instead of truncating the leaf digit, which conflicts with the key as normally stated.
- Splitting a stem into three rows — only two-way and five-way splits divide the ten possible leaves evenly.
Related Free Tools From Arb Digital
Bin the same data into bars with the histogram calculator, count occurrences with the frequency distribution calculator, get the quartiles and fences with the box plot calculator, read the centre with the mean, median and mode calculator, or locate a cut point with the percentile calculator. Everything else is on the free online tools hub.
Frequently Asked Questions
A display in which each value is split into leading digits, the stem, and a final digit, the leaf. Stems are listed down the left and their leaves in sorted order to the right, showing the distribution's shape while keeping every value.
It states how to reconstruct an original value from a stem and a leaf. A key reading 3 | 4 = 34 tells you the leaf is the units digit; the same display with a key of 3 | 4 = 3.4 means something ten times smaller.
When the data clusters into very few stems, so each row carries a long string of leaves and no shape is visible. Splitting each stem into two rows, one for leaves 0 to 4 and one for 5 to 9, restores the detail.
Yes. Leaving a stem out closes a real gap in the data and makes the distribution look more continuous than it is. Empty rows are part of the picture.
Truncate. The usual convention drops the extra digits rather than rounding them, so 34.7 appears as stem 3, leaf 4 when the leaf unit is 1.
Yes. Because the leaves are sorted and every value is kept, counting in from either end lands you on the middle value directly, which is one of the display's main advantages over a histogram.
Roughly fifteen to a hundred and fifty values. Below that there is too little to show a shape; above it the rows grow too long to read and a histogram is the better choice.
This tool is provided for educational use. Leaf digits are truncated rather than rounded, so statistics read off the display can differ slightly from those computed on the raw data.
