## Content description

Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including 'skewed', 'symmetric' and 'bi modal' (ACMSP282)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

## Stem-and-leaf plots

**Numerical data** (quantitative data) consists of values in which there is a definite numerical order, for example, scores in a test or heights of students in a class.

A stem-and-leaf plot can be used to represent numerical data.

A stem-and-leaf plot represents the values of the data set in the form of a stem and a leaf.

The **stem **is the first digit of a two-digit number, or the first two digits of a three-digit-number, and so on.

The leaf is usually the last digit of the value.

#### Example 1

The marks out of 50 obtained by 16 students in a Mathematics test are:

43 | 24 | 29 | 19 | 11 | 14 | 25 | 17 | 32 | 27 | 29 | 7 | 14 | 19 | 39 | 49 |

Represent this information on a stem-and-leaf plot.

#### Solution

We use the first digit of each mark as the stem, writing 7 as 07.

0 | 7 | |

1 | 1 4 4 7 9 9 | |

2 | 4 5 7 9 9 | |

3 | 2 9 | |

4 | 3 9 | 3\(\mid\)2 represents a mark of 32 |

We can see that stem-and-leaf plots are useful for displaying the shape of the data and giving the reader a quick overview. They retain most of the raw numerical data and are useful for highlighting **outliers** and finding the **mode**.