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1.8 Graphical Representations of Summary Statistics

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The Five-Number Summary

The five-number summary describes a distribution with five values:

Min, Q1, Median, Q3, Max\text{Min},\ Q_1,\ \text{Median},\ Q_3,\ \text{Max}

Example: Data: 12, 15, 17, 19, 21, 23, 25, 26, 28, 35

Ordered: 12, 15, 17, 19, 21, 23, 25, 26, 28, 35

  • Minimum = 12
  • Q1{Q_1} = median of {12,15,17,19,21} = 17
  • Median = (21+23)/2=22{(21 + 23)/2 = 22}
  • Q3{Q_3} = median of {23,25,26,28,35} = 26
  • Maximum = 35
  • IQR = 26−17=9{26 - 17 = 9}
  • Lower fence = 17−1.5(9)=3.5{17 - 1.5(9) = 3.5} → no low outliers
  • Upper fence = 26+1.5(9)=39.5{26 + 1.5(9) = 39.5} → no high outliers

In this unit

10 lessons

  1. 1.1Introducing Statistics: What Can We Learn from Data?Preview lesson
  2. 1.2The Language of Variation: VariablesPreview lesson
  3. 1.3Representing a Categorical Variable with TablesPreview lesson
  4. 1.4Representing a Categorical Variable with GraphsPreview lesson
  5. 1.5Representing a Quantitative Variable with GraphsPreview lesson
  6. 1.6Describing the Distribution of a Quantitative VariablePreview lesson
  7. 1.7Summary Statistics for a Quantitative VariablePreview lesson
  8. 1.8Graphical Representations of Summary StatisticsThis lesson
  9. 1.9Comparing Distributions of a Quantitative VariablePreview lesson
  10. 1.10The Normal DistributionPreview lesson

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