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1.9 Comparing Distributions of a Quantitative Variable

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Comparing Center and Spread

When comparing two or more distributions of a quantitative variable, always address center and spread using the same statistics for each group.

For symmetric distributions → use mean and standard deviation:
xˉ1 vs. xˉ2s1 vs. s2\bar{x}_1 \text{ vs. } \bar{x}_2 \qquad s_1 \text{ vs. } s_2
For skewed distributions or those with outliers → use median and IQR:
M1 vs. M2IQR1 vs. IQR2M_1 \text{ vs. } M_2 \qquad \text{IQR}_1 \text{ vs. } \text{IQR}_2

Key phrases:

  • "On average, Group A scored [value] points higher than Group B."
  • "The scores in Group A are more consistent (less variable) than Group B."
  • "The distributions have similar centers but Group B is more spread out."

Always justify your choice of statistics (mean vs. median) based on shape and presence of 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 StatisticsPreview lesson
  9. 1.9Comparing Distributions of a Quantitative VariableThis lesson
  10. 1.10The Normal DistributionPreview lesson

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