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FM Spread

1.7 Box Plots and the Five Number Summary

The Box Plot

  • The box plot is a graphical tool used to analyse the shape, spread and outliers of a numerical distribution.
  • It consists of a box with the bottom drawn at the value of quartile 1 and the top at quartile 3, a line drawn through the box at the median and a line either end of the box drawn to the lower and upper fences.
  • If the median line is in the middle of the box, the distribution is approximately symmetric, if it is drawn closer to the bottom of the box, it is positively skewed, if it is drawn closer to the top of the box, it is negatively skewed.
  • If the distribution has any outliers, they are represented as dots or crosses at their respective value along the y-axis and placed parallel to box.
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1.6 Describing Numerical Distributions


  • The shape of a numerical distribution relies on two factors: symmetry and outliers.
  • If you can draw a vertical line through some point in the distribution whereby the distribution to the left of the line looks similar to a mirror image of the distribution to the right of it, it is an approximately symmetrical distribution. If this is not the case, the distribution is asymmetric.

Note: in some cases, you may find situations where the distribution has perfect symmetry. In these situations, you can drop the “approximately” term and refer to it simply as symmetrical.

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