# Line plots and stem-and-leaf plots

Most people are familiar with bar graphs, line graphs, and circle graphs. Here we will explain two kinds of plots that are used to visualize data.

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data.

**Example**

The following numbers are the result from a test taken by a class of 24 students:

$$16, 14, 17, 11, 14, 19, 11, 17, 12, 21, 22, 18, 11, 16, 15, 14, 18, 12, 13, 16, 17, 15, 13, 17$$

To make a line plot out of our data we determine a scale that includes all of the data in appropriate intervals. Then we plot each number using **X** or other marks to show the frequency:

$$\;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \, \;\, \, \, X\\ X\;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, \;\, \, \, X\;\, \, \, \;\, \, \, \;\, \, \, X\;\, \, \, X\\ X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\\ X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, X\;\, \, \, \;\,\: \: \: \, \, X \, \,\: \: X\\ ------------------------------\\11\, \, \, \,12\, \, \, \,13\, \, \, 14\, \, \, 15\, \, \, \: 16\, \, \, 17\, \, \, \: 18\, \, \, 19\, \, \, \, \, 20\, \, \, 21\, \, \, 22\, \, \, 23\\$$

A stem-and-leaf plots in statistics, is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.

The stem usually consists of the digits in the greatest common place value of each data while the leaves contain the other digits of each item of data.

**Example**

We return to the result from the last example:

16, 14, 17, 11, 14, 19, 11, 17, 12, 21, 22, 18, 11, 16, 15, 14, 18, 12, 13, 16, 17, 15, 13, 17

First we sort the results in ascending order:

11, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 19, 21, 22

Then we plot our stem-and-leaf plot:

$$\begin{tabular} {c | c c c c c c c c c c c c c c c c c c c c c} Stem & Leaf \\ 1 & 1&1& 1& 2& 2& 3& 3& 4& 4& 4& 5& 5& 6& 6& 6& 7& 7& 7& 7& 8& 8& \\ 2 & 1 & 2 \\ \end{tabular}$$

$$Stem\mid Leaf\\ 1\,\; \; \; \; \; \; \mid 1\;1\; 1\; 2\; 2\; 3\; 3\; 4\; 4\; 4\; 5\; 5\; 6\; 6\; 6\; 7\; 7\; 7\; 7\; 8\; 8\; 9\; \\ 2\,\; \; \; \; \; \, \mid 1\; 2$$

The stem is found in the left-hand column and contains our tens digits. The leaf, found in the right-hand column, shows all the ones digits for each of the tens and twenties. In order to determine our original values we simply connect our tens digits with our ones digits.

**Video lesson**

Construct a stem-and-leaf plot out of the following data: 6, 6,7,8,9,13,16,19,21,25,26