In general, we find that students tend to use normal and average interchangeably along with words like "typical", which causes them to not understand when normal is being used in statistics in strict reference to distributions. Research shows that this confusion is very frequently not resolved even after a student has completed an introductory course.

Student Notions

When presented with a prompt such as: "The values for a certain variable are known to have a normal distribution. What does normal mean in this context?", student responses have been summarized as including one or more of the following notions (in this case, categories are not exclusive):

  • Bell Shaped
  • Symmetric; Not Skewed
  • Mean in the middle; Mostly clustered around the mean
  • Following Empirical Rule; Standard Normal
  • Things that are equal, same, or equally/evenly distributed
  • Expected, likely, average, typical, common, acceptable
  • A function or model, random, sample size
  • Range/interval, standard deviation, confidence interval


The following HILT activities have been designed to address student misconceptions regarding "Normal" and have research that suggests they improve student learning:

IsAverageNormalImage.png WhyBeNormalImage.png
Is Average Normal? Why Be Normal?