Draw and describe a box and whisker plot. What is this used for?

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College Answer

This question has been asked previously and is covered well in previous examination reports 
and standard statistics texts. Candidates with knowledge of this topic did very well on this 
question. A few candidates described a Forest plot and scored poorly. Some candidates were 
able to draw the shape of the box and whiskers but expressed incorrect facts regarding what 
the line, the box and whiskers represented and thus lost marks. 

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

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).