Two varieties of runner bean are grown side by side on a garden allotment. As the pods are picked they are measured. The table gives the shortest pod, the l...

A box plot shows five figures: the two extremes at the ends of the whiskers, and the lower quartile, median and upper quartile making the box. The box holds the middle half of the data, so its width is the interquartile range, which measures spread while ignoring the extreme values.

1. Range and interquartile range for variety A [2 marks]
   \[\text{range} = \text{longest} - \text{shortest} = 38 - 12 = 26 \ \text{cm} \tag{1 mark}\] \[\text{IQR} = \text{upper quartile} - \text{lower quartile} = 29 - 18 = 11 \ \text{cm} \tag{1 mark}\]
2. Box plot for variety B [2 marks]
   Variety B has shortest 15, lower quartile 22, median 26, upper quartile 30 and longest 40, so the box runs from 22 to 30 with the median line at 26, and the whiskers reach out to 15 and 40. Drawn on the same scale beneath the plot for A:
3. Two comparisons [3 marks]
   A comparison must set the same measure side by side for both varieties, and say what it means.
   1. Average: the median for B is 26 cm against 23 cm for A, so B pods are on average about 3 cm longer.
   2. Spread: the interquartile range for B is \(30 - 22 = 8\) cm against \(29 - 18 = 11\) cm for A, so the middle half of the B pods is packed into a narrower band and B is the more consistent variety.
   The ranges tell a different story, \(40 - 15 = 25\) cm for B against 26 cm for A, which is why the interquartile range is the better measure of spread here: it is not distorted by a single unusually long or short pod.

Examination reminder: a comparison of box plots needs one statement about average and one about spread, each quoting the figures for both data sets; describing only one variety earns no comparison marks.