Overview of the Stem and Leaf Plot

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Data can be shown in a variety of ways including graphs, charts, and tables. A stem and leaf plot is a type of graph that is similar to a histogram but shows more information by summarizing the shape of a set of data (the distribution) and providing extra detail regarding individual values.

This data is arranged by place value where the digits in the largest place are referred to as the stem while the digits in the smallest value or values are referred to as the leaf or leaves, which are displayed to the right of the stem on the diagram.

Stem and leaf plots are great organizers for large amounts of information. However, it is also helpful to have an understanding of the mean, median and the mode of data sets in general, so be sure to review these concepts prior to beginning work with stem and leaf plots. 

Using Stem and Leaf Plot Diagrams

Stem and leaf plot graphs are usually used when there are large amounts of numbers to analyze. Some examples of common uses of these graphs are to track series of scores on sports teams, series of temperatures or rainfall over a period of time, and series of classroom test scores. Check out this example of test scores below:

Test Scores Out Of 100
  Stem  Leaf
  9  2 2 6 8
  8  3 5
  7  2 4 6 8 8 9
  6  1 4 4 7 8
  5  0 0 2 8 8

Here, the Stem shows the 'tens' and the leaf. At a glance, one can see that 4 students got a mark in the 90s on their test out of 100. Two students received the same mark of 92; that no marks were received that fell below 50, and that no mark of 100 was received.

When you count the total amount of leaves, you know how many students took the test. As you can tell, stem and leaf plots provide an "at a glance" tool for specific information in large sets of data. Otherwise one would have a long list of marks to sift through and analyze.

This form of data analysis can be used to find medians, determine totals, and define the modes of data sets, providing valuable insight into trends and patterns in large datasets that can then be used to adjust parameters that might affect those results.

In this instance, a teacher would need to ensure that the 16 students who made below an 80 truly understood the concepts on the test. Because 10 of those students failed the test, which accounts for almost half of the class of 22 students, the teacher might need to try a different method that the failing group of students could understand.

Using Stem and Leaf Graphs for Multiple Sets of Data

To compare two sets of data, you can use a "back to back" stem and leaf plot. For instance, if you wanted to compare the scores of two sports teams, you would use the following stem and leaf plot:

 Leaf Stem Leaf
 Tigers  Sharks
 0 3 7 9 3 2 2
 2 8 4 3 5 5
 1 3 9 7 5 4 6 8 8 9

The tens column is now in the middle, and the ones column is to the right and left of the stem column. You can see that the Sharks had more games with a higher score than the Tigers because the Sharks only had 2 games with a score of 32 while the Tigers had 4 games, a 30, a 33, a 37 and a 39. You can also see that the Sharks and the Tigers tied for the highest score of all — a 59.

Sports fans often use these stem and leaf graphs to represent their teams' scores to compare success. Sometimes, when the record for wins is tied within a football league, the higher-ranked team will be determined by examining data sets that are more easily observable here including the median and mean of the two teams' scores.

Stem and leaf graphs can be infinitely expanded to include multiple sets of data, but it could get confusing if not properly separated by stems. For comparing three or more sets of data, it's recommended that each data set is separated by an identical stem.

Practice Using Stem and Leaf Plots

Try your own Stem and Leaf Plot with the following temperatures for June. Then, determine the median for the temperatures:

77 80 82 68 65 59 61
57 50 62 61 70 69 64
67 70 62 65 65 73 76
87 80 82 83 79 79 71
80 77

Once you've sorted the data by value and grouped them by tens digit, put them into a graph labeled temperatures with the left column, the stem, labeled "Tens" and the right column labeled "Ones," then fill in the corresponding Temperatures as they occur above. Once you've done this, read on to check your answer.

How to Solve to Practice Problem

Now that you've had a chance to try this problem on your own, read on to see an example of the correct way to format this data set as a stem and leaf plot graph.

 Tens Ones
 5 0 7 9
 6 1 1 2 2 4 5 5 5  7 8 9
 7 0 0 1 3 6 7 7 9  9
 8 0 0 0 2 2 3 7

You should always begin with the lowest number, or in this case temperature: 50. Since 50 was the lowest temperature of the month, enter a 5 in the tens column and a 0 in the ones column, then observe the data set for the next lowest temperature: 57. As before, write a 7 in the ones column to denote that one instance of 57 occurred, then proceed to the next-lowest temperature of 59 and write a 9 in the ones column.

Then, find all of the temperatures that were in the 60's, 70's, and 80's and write each temperature's corresponding ones value in the ones column. If you've done it correctly, it should yield a steam and leaf plot graph that looks like the one on the left.

To find the median, count all the days in the month — which in the case of June is 30. Then divide 30 in half to get 15; then count either up from the lowest temperature 50 or down from the highest temperature of 87 until you get to the 15th number in the data set; which in this case is 70 (It is your median value in the dataset).