Stem-and-leaf displays can also be used to convey non-numerical information. A box plot or histogram may become more appropriate as the data size increases. With very large data sets, a stem-and-leaf display will become very cluttered, since each data point must be represented numerically. A dot plot may be better suited for such data. With very small data sets a stem-and-leaf displays can be of little use, as a reasonable number of data points are required to establish definitive distribution properties. However, stem-and-leaf displays are only useful for moderately sized data sets (around 15–150 data points). They are also useful for highlighting outliers and finding the mode. They retain (most of) the raw numerical data, often with perfect integrity.
Stem-and-leaf displays are useful for displaying the relative density and shape of the data, giving the reader a quick overview of the distribution. It is important to note that when there is a repeated number in the data (such as two 72s) then the plot must reflect such (so the plot would look like 7 | 2 2 5 6 7 when it has the numbers 72 72 75 76 77). The leaves are listed in increasing order in a row to the right of each stem. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The stems are listed to the left of the vertical line. The stem-and-leaf display is drawn with two columns separated by a vertical line. In this example, the leaf represents the ones place and the stem will represent the rest of the number (tens place and higher). The remaining digits to the left of the rounded place value are used as the stem. In the case of very large numbers, the data values may be rounded to a particular place value (such as the hundreds place) that will be used for the leaves. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. Next, it must be determined what the stems will represent and what the leaves will represent. To construct a stem-and-leaf display, the observations must first be sorted in ascending order: this can be done most easily if working by hand by constructing a draft of the stem-and-leaf display with the leaves unsorted, then sorting the leaves to produce the final stem-and-leaf display. Unlike histograms, stem-and-leaf displays retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order-based inference and non-parametric statistics.
A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line. Ī stem-and-leaf plot is also called a stemplot, but the latter term often refers to another chart type. This plot has been implemented in Octave and R. Modern computers' superior graphic capabilities have meant these techniques are less often used. The popularity during those years is attributable to their use of monospaced (typewriter) typestyles that allowed computer technology of the time to easily produce the graphics. Stemplots became more commonly used in the 1980s after the publication of John Tukey's book on exploratory data analysis in 1977.
They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis. A stem-and-leaf plot of prime numbers under 100 shows that the most frequent tens digits are 0 and 1 while the least is 9Ī stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.
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