# 1.6.1 - Dotplots, Stem-and-Leaf Diagrams

1.6.1 - Dotplots, Stem-and-Leaf Diagrams## Dotplot

A dot plot displays the data as dots on a number line. It is useful to show the relative positions of the data.

#### Dotplot Example

Each of the ten children in the second grade was given a reading aptitude test. The scores were as follows:

95, 78, 69, 91, 82, 76, 76, 86, 88, 79

Here is a dot plot for the data.

Each of the observations is represented as a dot. If there is more than one observation with the same value, a dot is placed above the others. A dotplot provides us with a quick glance at the data. We can easily see the minimum and maximum values and can see the mode is 76. Dotplots are generally used for small data sets.

##
Minitab^{®}

## Minitab: Dotplots

How to create a dotplot in Minitab:

- Click
`Graph`>`Dotplot` - Choose
`Simple`. - Enter the column with your variable
- Click
`OK`.

## Stem-and-Leaf Diagrams

To produce the diagram, the data need to be grouped based on the “stem”, which depends on the number of digits of the quantitative variable. The “leaves” represent the last digit. One advantage of this diagram is that the original data can be recovered (except the order the data is taken) from the diagram.

#### Stem-and-Leaf Example

Jessica weighs herself every Saturday for the past 30 weeks. The table below shows her recorded weights in pounds.

135 |
137 |
136 |
137 |
138 |
139 |

140 |
139 |
137 |
140 |
142 |
146 |

148 |
145 |
139 |
140 |
142 |
143 |

144 |
143 |
141 |
139 |
137 |
138 |

139 |
136 |
133 |
134 |
132 |
132 |

Create a Stem-and-Leaf Diagram for Jessica’s Weight.

**Answer**

The first step is to determine the stem. The weights range from 132 to 148. The stems should be 13 and 14. The leaves should be the last digit. For example, the first value (also smallest value) is 132, it has a stem of 13 and 2 as the leaf.

#### Stem-and-Leaf of weight of Jessica N = 30

#### Leaf Unit = 1.0

3 | 13 | 223 |

5 | 13 | 45 |

11 | 13 | 667777 |

(7) | 13 | 8899999 |

12 | 14 | 0001 |

8 | 14 | 2233 |

4 | 14 | 45 |

2 | 14 | 6 |

1 | 14 | 8 |

The first column, called depths, are used to display cumulative frequencies. Starting from the top, the depths indicate the number of observations that lie in a given row or before. For example, the 11 in the third row indicates that there are 11 observations in the first three rows. The row that contains the middle observation is denoted by having a bracketed number of observations in that row; (7) for our example. We thus know that the middle value lies in the fourth row. The depths following that row indicate the number of observations that lie in a given row or after. For example, the 4 in the seventh row indicates that there are four observations in the last three rows.

##
Minitab^{®}

## Minitab: Stem-and-Leaf Digrams

How to create a Stem-and-Leaf Diagram in Minitab:

- Click
`Graph`>`Stem-and-Leaf` - Enter the column with your variable
- Click
`OK`.