IB Mathematics SL 4.2 Understanding of box and whisker diagrams AA SL Paper 2- Exam Style Questions- New Syllabus
Janie claims that rabbits in Australia have longer ears than rabbits in Spain.
To test her claim, a randomly selected sample of rabbits was collected in each country.
The length of one ear of each rabbit was measured and the value recorded correct to the nearest millimetre (mm).
In the Australian sample, the median recorded value was 80 mm and the interquartile range was 11 mm.
The recorded values for the Spanish sample are shown in the following box and whisker diagram.
a) Complete the following table for the recorded values of the lengths of the rabbits’ ears in each sample [2]
bi) Justifying your answers, compare the distributions of the lengths of rabbits’ ears in Australia and Spain using the median [1]
bii) Justifying your answers, compare the distributions of the lengths of rabbits’ ears in Australia and Spain using the interquartile range [2]
▶️ Answer/Explanation
a) From the box plot, Spanish median is 75 mm, Q1 is 68 mm, Q3 is 84 mm. IQR is \( 84 – 68 = 16 \) mm.
Australia | Spain | |
Median (mm) | 80 | 75 |
Interquartile Range (mm) | 11 | 16 |
bi) Australian median is 80 mm, Spanish is 75 mm. Since 80 > 75, Australian rabbits have longer ears on average. [1]
bii) Australian IQR is 11 mm, Spanish is 16 mm. Since 16 > 11, Spanish rabbits show more variation in ear lengths. [2]