Within a whisker of panic
A The diagrams shown are called box-whisker plots or box-whisker graphs (sometimes called box plots for short). They are not difficult to understand once you know what the parts mean and they are useful when comparing two or more sets of data.
A box plot is a graphical representation of a set of data, and shows how that data is spread. In your diagram you have missed the line that appears across the box. The diagram consists then of a central box that represents the middle of the distribution of the data (called the interquartile range) extending from the lower quartile (25 per cent) to the upper quartile (75 per cent) of the data spread. A vertical line drawn through the box represents the median or middle value of the data. There are two tails (whiskers) on either side of the box. These show the lowest and highest values. The difference between these two extreme values provides the range of the data.
All this makes much more sense in context. Below are two box-whisker graphs from a player's time scores collected while playing the CD version of Perfect Times, my game for teaching and assessing fluency of multiplication tables. Before I discuss the comparisons I will explain how the data is collected. In this case a player has played their 6 times table (top graph) and their 10 times table (bottom graph). The time taken to play the game (including penalising incorrect answers) is recorded by the computer. These scores are then stored in a database and are accessible as box-whisker graphs. In these diagrams there is an extra line on each, in green, at the 20-second position; this is not part of the box-whisker plot but is a marker for the fluency of recall of the tables.
From the spread of the data around the green 20-second marker we can say that this pupil probably has instant recall of their 10 times table but not of their 6 times table. In particular because of the position of the boxes for the two times tables: the 10 times table box shows that almost 75 per cent of the time scores are below the 20-second fluency mark (the right-hand edge of the box is at 22 seconds) whereas in the 6 times table only about 25 per cent of the 31 scores collected (n=31) are below 20 seconds (the left-hand edge of box is at 21 seconds).
The median in the 10 times table, indicated by the red line, is 17 seconds.
Therefore, 50 per cent of the scores are 17 seconds or less - actually they are either 16 or 17 seconds for 25 per cent of the time (the lower quartile value is 16 seconds). The other 25 per cent of the player's fastest scores are between 14 and 16 seconds.
When we look at the 6 times table we can see that the left-hand edge of the box is at a time of 21 seconds. This means that 75 per cent of the scores are more than 21 seconds. The upper quartile of 28 seconds (right-hand edge of the box) suggests that 25 per cent of the scores are greater than 28 seconds. Half of the scores are between 21 and 28 seconds, so the player is fairly consistent, but they have not yet reached fluency.
The ranges of 20 seconds for the 6 times table (38-18) and 68 seconds for the 10 times table (82-14) don't tell us much about the player's fluency.
In this game the range tends to show how much a player has improved: the maximum score is often one of their first scores when getting to grips with the times table, but there can be other reasons.
The game is available to play at www.perfect-times.co.uk. When logged in, the results page shows players their own dynamic box-whisker plots, which are created from their time scores.
You might also find it helpful to go to www.duncanwil.co.ukboxplot.html
where Duncan Williamson describes a box-whisker plot and also how they can be obtained by entering data on to an Excel spreadsheet.
Perfect Times CD-Rom details can be found at www.cambridge.org
Email your questions to Mathagony Aunt at firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX