## 5.1 Quick revision

An Australian study compared the dimensions of jellyfish at two sites at Hawkesbury River, NSW (Dangar Island; Salamander Bay) to determine the difference between the jellyfish at each site. A histogram of the breadth of jellyfish at Dangar Island Bay is shown in Fig. 5.1.

1. Two students are arguing about the median breadth. Who is correct?

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: $$4$$ mm 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 $$4$$ mm.

1. Describe the histogram.
2. A boxplot comparing the breadths of jellyfish at Dangar Island and Salamander Bay is shown in Fig. 5.2. Describe and compare the breadths of the jellyfish.
3. Which box in the boxplot represents the Dangar Island jellyfish (shown in Fig. 5.1)?
1. Discuss in class.
2. The sample is small, so hard to too certain: Average about $$10$$ mm; data from about $$6$$ to $$16$$ mm; slightly right skewed; no outliers..
3. Discuss in class.

### References

Lunn AD, McNeil DR. Computer-intensive data analysis. Chichester: John Wiley; Sons; 1991.