What is a Stem-and-Leaf Plot?
A stem-and-leaf plot is a method of organizing quantitative data that visually represents the distribution of values while preserving the original numerical data. It separates each data point into a "stem" (the leading digit(s)) and a "leaf" (the trailing digit), arranging them in a way that resembles a bar graph turned on its side.
How to Construct a Stem-and-Leaf Plot
To create one, first separate each data value into its stem and leaf components; for example, in the number 23, '2' is the stem and '3' is the leaf. List all unique stems vertically in ascending order. Then, for each stem, list all corresponding leaves horizontally in ascending order. A key must be included to explain how to read the plot (e.g., "2|3 = 23").
A Practical Example
Consider the test scores: 65, 72, 78, 81, 83, 83, 85, 90, 91, 95. The stems would be 6, 7, 8, 9. The plot would look like: 6|5; 7|2 8; 8|1 3 3 5; 9|0 1 5. This clearly shows that most scores are in the 80s, and the lowest is 65, while preserving each score's exact value.
Importance and Applications
Stem-and-leaf plots are valuable for quickly displaying the shape, center, and spread of a data set, especially for smaller data sets. Unlike histograms, they retain the individual data values, which can be useful for identifying outliers or specific data points. They are commonly used in introductory statistics and for initial data exploration.