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Leaf and Stem Diagrams

In statistics, a stemplot (or stem-and-leaf plot) is a graphical display of quantitative data that is similar to a histogram and is useful in visualizing the shape of a distribution. They are generally associated with the Exploratory Data Analysis (EDA) ideas of John Tukey and the course Statistics in Society (NDST242) of the Open University, although in fact Arthur Bowley did something very similar in the early 1900s. Unlike histograms, stemplots: retain the original data (at least the most important digits) put the data in order - thereby easing the move to order-based inference and non-parametric statistics. A basic stemplot contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves.

Constructing a stemplot To construct a stemplot, the observations must first be sorted in ascending order. Here is the sorted set of data values that will be used in the example: 54 56 57 59 63 64 66 68 68 72 72 75 76 81 84 88 106 Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large or very small numbers, the data values may be rounded to a particular place value (such as the hundreds place) that will be used for the leaves. The remaining digits to the left of the rounded place value are used as the stems.

In this example, the leaf represents the ones place and the stem will represent the rest of the number (tens place and higher). The stemplot is drawn with two columns separated by a vertical line. The stems are listed to the left of the vertical line. 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 leaves are listed in increasing order in a row to the right of each stem.

5 | 4 6 7 9 6 | 3 4 6 8 8 7 | 2 2 5 6 8 | 1 4 8 9 | 10 | 6

key: 5|4=54 leaf unit: 1.0 stem unit: 10.0

For negative numbers, a negative is placed in front of the stem unit, which is still the value X / 10. Non-integers are rounded. This allowed the stem and leaf plot to retain its shape, even for more complicated data sets. As in this example below:

-2 | 4 -1 | 2 -0 | 3 0 | 4 6 6 1 | 7 2 | 5 3 | 4 | 5 | 7

Which represents the set of data:

-23.678758, -12.45, -3.4, 4.43, 5.5, 5.678, 16.87, 24.7, 56.8

Box Plot