## 4.2 Understanding histograms and boxplots

An Australian study (Lunn and McNeil 1991) compared the dimensions of jellyfish at two sites at Hawkesbury River, NSW (Dangar Island; Salamander Bay) to determine how the jellyfish were different at each site.

A histogram of the breadth of jellyfish at Dangar Island Bay is shown in Fig. 4.2.

- Two students are arguing about the median breadth.

**Student 1** says:

The bars in the histogram have heights of 10, 2, 4, 2 and 4.

When these numbers are put in order, they are: 2, 2, 4, 4, 10.

The median breadth is the median of these numbers, so the median breadth is the middle one: 4mm is the median.

**Student 2** responds:

You have the correct answer, but for the wrong reason!

There are five bars, and the middle bar is the third bar.

Since the third bar has a height of 4, the median breadth is 4mm.

Who is correct? Explain.

Describe the histogram.

A boxplot comparing the breadths of jellyfish at Dangar Island and Salamander Bay is shown in Fig. 4.3. Which box represents the Dangar Island jellyfish (shown in Fig. 4.2)?

Describe and compare the breadths of the jellyfish.