Stem and Leaf Plot Maker

How the stems and leaves are cut

The leaf is exactly one digit, the one at the leaf unit's place; the stem is every digit above it. With the leaf unit 1, 37 is stem 3 and leaf 7 (key 3 | 7 = 37); 142 is stem 14, leaf 2. With the leaf unit 0.1, 4.3 is stem 4, leaf 3 (key 4 | 3 = 4.3); with the unit 10, 1,250 is stem 12, leaf 5, which stands for 1,250 (key 12 | 5 = 1250).

Digits below the leaf are truncated, not rounded. At the unit 0.1, 4.25 becomes 4 | 2 (4.2) and 5.07 becomes 5 | 0 (5.0), the way most textbooks and the TI and Minitab stem-plots do it. The page says how many values were cut and shows the first few. If that loses something you care about, pick a smaller leaf unit. The median, quartiles, mode and range are worked out from your exact values, so they never suffer from the truncation; when it changes them, the page also gives the figures read from the plot's own truncated values, so you can see the difference.

The automatic unit is the smallest one that gives 20 stems or fewer, and never smaller than the decimals you typed (at most 0.001). Test scores from 52 to 97 get the unit 1 (stems 5 to 9). 4.25, 4.3 and 5.07 get the unit 0.01 (stems 42 to 50, nothing truncated); pick 0.1 for the shorter plot with stems 4 and 5. Change it whenever your class asks for a particular unit. Empty stems between the lowest and highest are kept, because the gaps are part of the picture.

Split stems, back to back and negatives

• Two lines per stem (a split or double stem plot): the first line of each stem holds leaves 0 to 4, the second 5 to 9. Five lines per stem hold 0–1, 2–3, 4–5, 6–7 and 8–9. Each line repeats the stem number, so nothing has to be decoded.
• Back to back: both sets share the stems in the middle. The right-hand set's leaves read left to right as usual; the left-hand set's leaves read right to left, smallest next to the stem. The key names both sides.
• Negative numbers get negative stems, plus a −0 stem for values between −9 and 0 (at the unit 1): −12 sits on the −1 stem with leaf 2, −7 on the −0 stem with leaf 7, and 7 on the 0 stem. Values grow down the page, so on a negative stem the larger leaf comes first: -1 | 5 2 means −15 then −12.

A worked example

Twenty test scores: 52 58 61 63 64 67 70 71 72 74 75 77 78 81 83 85 86 88 92 97. With the leaf unit 1 the plot is

5 | 2 8
6 | 1 3 4 7
7 | 0 1 2 4 5 7 8
8 | 1 3 5 6 8
9 | 2 7

and the key is 5 | 2 = 52. There are 20 values, so the median is halfway between the 10th and 11th: (74 + 75) / 2 = 74.5. The lower half is the first ten values, whose middle pair is 64 and 67, so Q1 = 65.5; the upper half's middle pair is 83 and 85, so Q3 = 84. The range is 97 − 52 = 45, and there is no mode, because no score appears twice. Split over two lines, the 7 stem becomes 7 | 0 1 2 4 and 7 | 5 7 8, which shows the bunch in the low 70s.

Which quartile method

The median, minimum, maximum, range and mode are the same everywhere. Q1 and Q3 are not: the page offers the same four methods as the Box Plot Maker, using the very same code, so a box plot drawn there from the same numbers agrees with what you read here. The default, the median of each half with the median left out when the count is odd, is the rule TI-83/84 calculators and most textbooks use. Excel's QUARTILE.INC (and Google Sheets' QUARTILE) and QUARTILE.EXC interpolate between neighbours and may give values that are not on the plot. The chosen method is defined under its menu.

What it cannot do

• At most two data sets (one each side of a back-to-back plot). For three or more groups, draw box plots side by side.
• At most 1,000 values in all; beyond that only the first 1,000 are plotted and the page says so. A plot also stops at 200 lines; pick a larger leaf unit if it asks.
• Leaves are one digit. There are no two-digit leaves (like 3 | 25); use a smaller leaf unit and longer stems instead.
• Values are truncated to the leaf, never rounded. If your teacher rounds, round the numbers first and paste those.
• Numbers of one billion or more in size are left out, and only the first six decimals of a number are read.
• The PNG and SVG use the fonts of the device that opens them (Geist Mono where installed, otherwise a system monospace font).

Privacy

Your numbers never leave your device: the plot is cut and drawn by code in this page, exports are made in the browser, and nothing is stored. The page sends an anonymous page-view count and, at most, two fixed words (stem-make, stem-export), never a number or a name.

Questions

How do you make a stem and leaf plot with decimals?

Choose the place of the leaf. For 4.25, 4.3 and 5.07 with the leaf at 0.1, the stem is the whole-number part and the leaf is the tenths digit: 4 | 2 3 and 5 | 0, with the key 4 | 2 = 4.2. The hundredths digits of 4.25 and 5.07 are cut off (truncated), not rounded, so 4.25 is shown as 4.2 and 5.07 as 5.0. Put the leaf at 0.01 instead and the stems become 42, 43 and 50 and nothing is lost.

What is a split stem and leaf plot?

Each stem is written on two lines, the first holding leaves 0 to 4 and the second leaves 5 to 9, so data that crowds onto a few stems spreads out and its shape shows. With five lines per stem the leaves go 0–1, 2–3, 4–5, 6–7 and 8–9. Use it when most values share two or three stems.

How do you read a back to back stem and leaf plot?

The stems run down the middle. The second data set's leaves grow to the right as usual; the first set's leaves grow to the left, so they read right to left, smallest next to the stem. 8 6 2 1 | 3 | 3 7 means 31, 32, 36, 38 in the left set and 33, 37 in the right set.

How are negative numbers shown in a stem and leaf plot?

With negative stems, and a separate −0 stem for values between −9 and 0, because −7 has stem −0 and leaf 7 while 7 has stem 0 and leaf 7. So −12 goes on the −1 stem and −7 on the −0 stem. This page lists the values smallest first: on a negative stem the larger leaf comes first, -1 | 5 2 means −15 and −12.

How do you find the median and quartiles from a stem and leaf plot?

The leaves are already in order, so count in from either end. With n values the median is the value at position (n + 1) / 2. Q1 and Q3 depend on the method: most textbooks and TI calculators take the median of the lower and upper halves, leaving the median out when n is odd. The page uses the same four methods as the Box Plot Maker, so its box plot of the same data agrees.