# Stem-and-Leaf Plots

A stem & leaf plot organizes data points by the place value of the leading digits. When making a stem & leaf plot, each item of data is separated into two parts. The “stems” usually consist of the digits in the greatest common place value of each item of data. The “leaves” contain the other digits of each item of data.

For example, suppose you're given the data set $\text{{35,37,23,24,27,31,33,49,34,35,41}}$ . The tens digits would be the "stems", and the ones digits would be the "leaves". The smallest tens digit is $\text{2}$ , and the greatest is $\text{4}$ ; write them in vertically on the left. Then, for each stem, write the leaves in increasing order on the right:

$\begin{array}{cc}\begin{array}{l}\text{Stem}\hfill \\ 2\text{\hspace{0.17em}}\hfill \\ 3\text{\hspace{0.17em}}\hfill \\ 4\text{\hspace{0.17em}}\hfill \end{array}& |\begin{array}{l}\text{Leaf}\hfill \\ 3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}7\hfill \\ 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}5\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}5\text{\hspace{0.17em}}\text{\hspace{0.17em}}7\hfill \\ 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}9\hfill \end{array}\end{array}$

Note that there are two $\text{5}$ 's in the second row, since there are two $\text{35}$ 's in the data set.

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Example:
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Make a stem-and-leaf plot for the data set below. Use it to find the median, mode, and range of the data set.

$\begin{array}{l}\text{{0}\text{.1325,0}\text{.1329,0}\text{.1331,0}\text{.1332,0}\text{.1332,0}\text{.1333,0}\text{.1337,}\\ \text{0}\text{.1344,0}\text{.1348,0}\text{.1351}}\end{array}$ .

Note that in this case, the data set is already in order from least to greatest. (This may not always be the case.)

The digits $0.13$ are common to all data points. So arrange $\text{0}\text{.132,0}\text{.133,0}\text{.134,}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0.135$ in the left column.

$\begin{array}{c}132\\ 133\\ 134\\ 135\end{array}|\begin{array}{ccccc}5& 9& & & \\ 1& 2& 2& 3& 7\\ 4& 8& & & \\ 1& & & & \end{array}$

Be sure to include a "key" to show the place value that is meant. In this case:

${132}{|}{5}{=}{0.1325}$

There are $\text{10}$ elements in this set, an even number. So the median of the data is the mean of the ${5}^{\text{th}}$ and ${6}^{\text{th}}$ numbers. Counting on the stem and leaf plot, we see that $133$ | $2$ and $133$ | $3$ are the ${5}^{\text{th}}$ and ${6}^{\text{th}}$ entries. So, the median is

$\frac{0.1332+0.1333}{2}=0.13325$

To find the mode of the data set, just look for the "leaf" which is repeated the most times under a single "stem". In this case, $133$ | $2$ occurs twice. So the mode is $\text{0}\text{.1332}$ .

To find the range of the data set, subtract the least number from the greatest.

$0.1351-0.1325=0.0026$

The range is $0.0026$ .