## 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.