Create a Stem and Leaf Diagram

Also known as a stemplot, this type of diagram is an easy way to arrange a group of numbers (or data set) to better display information. Back-to-back stem and leaf diagrams can be used to compare two data sets.

Steps

Create a Simple Stem and Leaf Diagram

  1. Rewrite your data in numerical order. This is especially helpful for numbers with 3 digits or more so you can determine which stem is best to use, but useful for all data sets.
  2. Identify the stem for each number. The stem digits always come before the leaf digits. In most cases, the stem is every digit except for the last one.
    • For a data set with only 2 digit numbers (such as 48 or 1.2) always use the first digit as the stems.
  3. Write out your stems in a vertical column labeled "stem". Include any numbers that fall between two stems, even if there are no numbers in your data that begin with that stem. (For instance, in the example image, 10 is included even though none of the numbers begin with those digits.)
    • If your stems are more than one digit long and you find yourself including more than a couple stems with no associated numbers, consider starting again with a smaller stem.[1]
  4. Identify the leaf for each number. Any digits you didn't include in the stem belong in the leaf.
  5. Make a leaf column and add your first number's leaf to it. First find the first number's stem in the Stem column. In the Leaf column across from it, add your number's leaf.
  6. Fill out the rest of your leaf column the same way. Each row in the leaf column should be sorted in numerical order (lowest number to highest number).
    • If a number is repeated, write it down as many times as it appears.
    • If your leaves have more than one digit, make sure to separate them from each other with spaces.
  7. Finish by adding a key below or above your diagram to explain it. Write any number in your data set as you see it on the stem and leaf diagram, including the vertical line. After it, write = and then the number as it looked originally. This tells people how to read your stem and leaf diagram.
    • This may seem unnecessary, but comes in handy when you're using decimal points (or in certain other situations). For example, if one of your values is 4.5, you can write that as 4 | 5 and explain in your key that 4|5 = 4.5.

Create a Back to Back Stem and Leaf Diagram

  1. Reorder each of the two sets of data. Keeping them separate, rewrite them as two lists in numerical order.
  2. Following the instructions in Method 1, make a stem and leaf diagram for one set of data.
    • NOTE: Make sure to leave space on the left side of the page for another column!
    • NOTE: Skip step 7 (the Key). We'll get to that later in this method.
  3. Using the same method, make a second leaf column on the left-hand side of the stem column.
    • Add additional rows to the diagram if there are stems in the second data plot that don't yet have a row.
  4. Finish by adding two keys, one next to each leaf column.[2] For each key, write any number in your data set as you see it on the stem and leaf diagram, including the vertical line. After it, write = and then the number as it looked originally. This tells people how to read each column of your stem and leaf diagram.
    • NOTE: The two keys should look different, since the diagram displays one data set in "leaf stem" order and the other in "stem leaf" order. (See the example image.)
    • This may seem unnecessary, but comes in handy when you're using decimal points (or in certain other situations). For example, if one of your values is 4.5, you can write that as 4 | 5 and explain in your key that 4|5 = 4.5.

Tips

  • If you have too many leaves in one row, you can split up a single stem into more than one row! Say your diagram has a lot of rows like this: 2|0011234445778889. Instead make each row cover five numbers (20-24 and 25-29) and write two rows: 2(0)|001123444 and 2(5)|5778889.[3]
  • Stem and leaf diagrams are useful for displaying how the data is distributed without losing any information.[4]

Related Articles

Sources and Citations

  1. ↑ http://mathworld.wolfram.com/Stem-and-LeafDiagram.html
  2. ↑ http://www.sophia.org/tutorials/back-to-back-stem-and-leaf-plots--4
  3. ↑ http://www.purplemath.com/modules/stemleaf2.htm
  4. ↑ http://www.purplemath.com/modules/stemleaf.htm

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