Sampling distributions of the mean


This file contains a collection of clicker questions that target concepts on sampling distribution of the mean.

Prerequisite Knowledge

  • be able to recognize probability models as distributions with shape, centre, and spread
  • be able to recall key properties of the Normal model
  • be able to distinguish between a population and a sample, and between parameters and statistics

Learning Objectives

  • Identify the population, sample, parameters and statistics in a given scenario
  • Recall the sampling distribution of the mean of a sample from a Normal distribution
  • Describe properties of the sampling distribution of the sample mean in general situations, using the Central Limit Theorem
  • For the sample mean, explain whether and how the population distribution and the sample size influence the sampling distribution of the sample mean
  • Apply the Central Limit Theorem to problems involving averages of variables from arbitrary distributions


These clicker questions target concepts on the sampling distribution of the mean.  They also address common misconceptions (e.g., confusion between the distribution of data from a random sample and the sampling distribution of the mean, misapplication of Central Limit Theorem in describing the shape of the distribution of data from a random sample). 

Suggested Uses, Tips and Discoveries

These resources are intended to be used in a number of ways:

  • as stand-alone clicker questions during lectures;
  • as assessment questions during and outside of class (e.g., pre-lecture quiz after students complete pre-lecture reading or other assigned tasks);
  • as questions to be adapted for use in guided in-class activities or other instructor-supplied material


  • Yu, Eugenia
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