1. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 2.4 Box and whisker plots

2. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots A box and whisker plot is a simple yet effective way of presenting important information about data. It consists of five parts, as shown in the diagram below. minimum value lower quartile upper quartile median maximum value

3. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots Box and whisker plots from discrete data The data below represents the shoe sizes of 30 students in a class. 42 38 44 42 43 38 36 40 45 44 39 42 38 41 40 43 45 46 39 42 41 38 39 44 43 42 39 36 38 40 These should be arranged in order of size. 36 36 38 38 38 38 38 39 39 39 39 40 40 40 41 41 42 42 42 42 42 43 43 43 44 44 44 45 45 46

4. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots 36 36 38 38 38 38 38 39 39 39 40 40 40 41 41 42 42 42 42 42 43 43 44 44 44 45 45 46 The median value is the middle one. If there are n results the middle value is found at result The median value here is therefore at i.e. midway between the 15th and 16th results. The median value is 41.

5. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots 36 36 38 38 38 38 38 39 39 39 39 40 40 40 41 41 42 42 42 42 42 43 43 43 44 44 44 45 45 46 The lower quartile value is at the quarter mark. If there are n results the lower quartile value is found at result The lower quartile value here is therefore at i.e. between the 7th and 8th results. The lower quartile is 38.5.

6. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots 36 36 38 38 38 38 38 39 39 39 39 40 40 40 41 41 42 42 42 42 42 43 43 43 44 44 44 45 45 46 The upper quartile value is at the three-quarter mark. If there are n results the upper quartile value is found at result The upper quartile value here is therefore at i.e. between the 23rd and 24th results. The upper quartile is 43.

7. Mathematical Studies for the IB Diploma Second Edition © Hodder & Stoughton Ltd 2012 Box and whisker plots The analysis of the data can be summarized as follows. – Minimum value = 36 – Lower quartile = 38.5 – Median = 41 – Upper quartile = 43 – Maximum value = 46 36 37 38 39 40 41 42 43 44 45 46