Prerequisite
It is helpful to have an understanding of the mean, median and the mode prior to beginning work with Stem and Leaf Plots.
What is 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. The Stem-and-Leaf Plot summarizes the shape of a set of data (the distribution) and provides extra detail regarding individual values. The data is arranged by place value. The digits in the largest place are referred to as the stem and the digits in the smallest place are referred to as the leaf (leaves). The leaves are displayed to the right of the stem. Stem and Leaf Plots are great organizers for large amounts of information.
What Are They Used For?
They are usually used when there are large amounts of numbers to analyze. Series of scores on sports teams, series of temperatures or rainfall over a period of time, series of classroom test scores are examples of when Stem and Leaf Plots could be used.
What Does a Stem and Leaf Look Like?
Example:
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 |
What does this Stem and Leaf Plot Show?
The Stem shows the 'tens' and the leaf. At a glance, one can see that 4 students got a mark in the 90's on their test out of 100. Two students received the same mark of 92. No marks were received below 50. No mark of 100 was received. When you count the total amount of leaves, you know how many students took the test. The information is nicely organized when a Stem and Leaf Plot is used. 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.
More Than One Set 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:
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 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. The Sharks only had 2 games with a score in of 32. The Tigers had 4 games, a 30, a 33, a 37 and a 39. You can also see that the Sharks had the highest score of all - a 59, compared to the Tigers with a 57.
Stem and Leaf Plots enable you to find medians, determine totals, and determine the modes.
Try your own Stem and Leaf Plot with the following temperatures for June. 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
Solution:
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 |
Begin with the lowest temperature.
The lowest temperature of the month was 50. Enter the 5 in the tens column and a 0 in the ones column. What's the next lowest temperature? It's 57, enter a 7 in the ones column, next is 59, enter a 9 in the ones column.
Now, find all of the temperatures that were in the 60's, 70's and 80's.
Enter the rest of the temperatures sequentially until your Stem and Leaf Plot contains all of the data. It should look like the one on the left.