Draw and describe a box and whisker plot. (50% of marks) What is this used 
for? (50% of marks)

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College Answer

Candidates either knew this topic or knew nothing about it. Some confused this with a Forrest 
plot which scored no marks. This topic is well covered in many standard statistics books such as
Statistical methods for anaesthesia and intensive care / P S Myles, T Gin – 1
st Ed - Oxford: 
Butterworth-Heinemann, 2001 ISBN: 9780750640657

Discussion

The box and whisker plot is a way of graphically representing the "five number summary", or four parameters which demonstrate the central tendency of the data set. Correctly, the examiners point out that answering this question with a description of a forest plot would be disastrous.

The parameters:

  • Range (the minimum and maximum values)
  • First quartile (25%)
  • Third quartile (75%)
  • Median, represented by the vertical bar in the centre

Uses of this graph:

  • Good for comparing distributions (the centre, spread and overall range are immediately apparent)
  • Useful for indicating whether a distribution is skewed 
  • Detects outliers
  • Useful for summarising a set of data measured on an interval scale

References

Larsen, Russell D. "Box-and-whisker plots." J. Chem. Educ 62.4 (1985): 302.

Weisstein, Eric W. "Box-and-whisker plot." From MathWorld–A Wolfram Web Resource.[Cited 2006 June 7]. Available from: URL: http://mathwold. wolfram. com/Box-and-Whiskerplot (1999).