How to Understand a Stem and Leaf Plot Diagram

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 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 a series of scores on sports teams, a series of temperatures or rainfall over a period of time, or a series of classroom test scores. Check out this example of test scores: 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 The Stem shows the tens column and the leaf. At a glance, you can see that four students got a mark in the 90s on their test out of 100. Two students received the same mark of 92, and no students received marks that fell below 50  or reached 100. When you count the total number of leaves, you know how many students took the test. Stem-and-leaf  plots provide an at-a-glance tool for specific information in large sets of data. Otherwise, you would have a long list of marks to sift through and analyze. You can use this form of data analysis to find medians, determine totals, and define the modes of data sets, providing valuable insight into trends and patterns in large data sets. In this instance, a teacher would need to ensure that the 16 students who scored below 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 want to compare the scores of two sports teams, you can use the following stem-and-leaf plot:   Scores 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 column, 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 two games with a score  of 32, while the Tigers had four games—a 30, 33, 37 and a 39. You can also see that the Sharks and the Tigers tied for the  highest score:  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, including the median and mean of the two teams scores. 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 6157 50 62 61 70 69 6467 70 62 65 65 73 7687 80 82 83 79 79 7180 77 Once youve sorted the data by value and grouped them by the tens digit, put them into a graph called Temperatures. Label the left column (the stem) as Tens and the right column as Ones, then fill in the corresponding temperatures as they occur above. How to Solve to Practice Problem Now that youve 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. Temperatures 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 indicate that one instance of 57  occurred, then proceed to the next-lowest temperature of 59 and write a 9 in the ones column. Find all of the temperatures that were in the 60s, 70s, and 80s and write each temperatures corresponding ones value in the ones column. If youve done it correctly, it should yield a stem-and-leaf  plot graph that looks like the one in this section. To find the median, count all the days in the month, which in the case of June is 30. Divide 30 by two, yielding 15, count either up from the lowest temperature of 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. This is your median value in the data set.