Stem and Leaf Plot Generator: Stem-and-Leaf Display with Median, Mode and Key
Make a stem-and-leaf plot from a list of numbers, with split stems, decimals, negatives and back-to-back plots, plus the key, median, mode, mean and range.
How it works
value = stem × 10 × leaf unit + leaf × leaf unit · median = middle value (n odd) or average of the two middle values (n even) · mode = most frequent value · mean = Σx ÷ n · range = max − min
A stem-and-leaf plot splits each number into a leaf, its last shown digit, and a stem, all the digits in front of it. With a leaf unit of 1, the value 47 has stem 4 and leaf 7. Stems are written once in a column, smallest first, with any empty stems in between kept, and the leaves of every value with that stem are listed in order to its right. The result looks like a histogram turned on its side but keeps every original value, so you can still read the minimum, maximum, median and mode straight off the plot. The key (for example 9 | 5 = 95) tells readers what the digits mean. The calculator picks the leaf unit automatically from your data (or you can set it): 0.1 for data like 3.7 and 4.2, 10 for data in the hundreds, and so on. Digits beyond the leaf unit are cut off, as is standard, but the statistics use the exact values. Split stems into 2 or 5 rows when the data bunch on a few stems, add a second list under More options for a back-to-back plot, and use negative numbers freely: they get negative stems, including a “-0” stem. Compared with a box plot or a frequency table, which summarize the data, a stem-and-leaf display keeps each value visible.
Worked example
For the 20 test scores 78, 85, 92, 67, 74, 88, 95, 81, 73, 69, 84, 90, 77, 86, 79, 58, 82, 91, 76, 88, the automatic leaf unit is 1, so the tens digit is the stem and the ones digit the leaf. The plot has 5 rows: 5 | 8; 6 | 7 9; 7 | 3 4 6 7 8 9; 8 | 1 2 4 5 6 8 8; 9 | 0 1 2 5. With 20 values the median is the average of the 10th and 11th values in order, (81 + 82) ÷ 2 = 81.5. The mode is 88 (it appears twice), the mean is 1,613 ÷ 20 = 80.65, the range is 95 − 58 = 37, and the key reads 9 | 5 = 95.
Sources: CalculatorSoup: Stem and leaf plot generator (worked examples)
Frequently asked questions
How do you make a stem and leaf plot?
Sort the data, choose the leaf unit (usually the ones digit), split each value into a stem (the leading digits) and a leaf (the last digit), write the stems in a column from smallest to largest, and list each value’s leaf beside its stem in order. Add a key such as 4 | 7 = 47.
How do you find the median from a stem and leaf plot?
Count the leaves to get n. If n is odd, count to leaf number (n + 1) ÷ 2; if n is even, average leaves n ÷ 2 and n ÷ 2 + 1. The cumulative column in the table makes the counting easy.
How do you show decimals in a stem and leaf plot?
Make the last decimal digit the leaf. For 3.7, 4.2 and 4.9 the leaf unit is 0.1, the stems are 3 and 4, and the key reads 4 | 2 = 4.2. For data with two decimals, either use a leaf unit of 0.01 or cut the values to one decimal.
What is a split stem and leaf plot?
Each stem is used for two rows, one for leaves 0–4 and one for leaves 5–9 (or five rows of two leaves each). It spreads out data that pile up on only a few stems, so the shape of the distribution is easier to see.
What is a back-to-back stem and leaf plot?
Two data sets share one column of stems: one set’s leaves go to the right, the other’s to the left, read outward from the stem. It is a quick way to compare two groups, such as two classes’ test scores.
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This calculator is for educational purposes. Double-check important results before acting on them.