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Measures of spread

Five number summaries

  • The five number summary for a data set is: the minimum, the first quartile, median, the third quartile and the maximum values in that order.
  • The box and whisker plot is the visual representation of the \(5\) number summary, see below.
  • For example, the five number summary of the data \((50\), \(55\), \(55\), \(55\), \(62\), \(65\), \(78\), \(99)\) is: \(50\), \(55\), \(58.5\), \(71.5\), \(99\).
  • Therefore the minimum is \(50\), the first quartile is \(55\), the median is \(58.5\), the third quartile is \(71.5\) and the maximum is \(99\). 
  • Remember that if the data set has units (e.g. cm or kg) you need to have units after each number.