Lesson 6.1 – What is a Sampling Distribution?

  • Distinguish between a parameter and a statistic. 
  • Create a sampling distribution using all possible samples from a small population.
  • Use the sampling distribution of a statistic to evaluate a claim about a parameter. 

 

Activity: Guess the Midterm Average and Guess the Midterm Average Part 2

Chapter 6 introduces the idea of a sampling distribution.  To introduce this, we looked at all of the semester 1 midterm exam scores.  We began by showing students the entire population of scores and asked them to make a guess of what they thought the average score was on the exam.  As a class we talked about how we wouldn’t want to add up all the scores since there were 119 scores so instead we decided we would take samples of size 5 and find the average of each.  We made a dotplot of the sample means and used that to estimate the midterm mean.  You could do this with any set of data but we suggest using your own exam scores.

To drive home the point that each dot in sampling distribution now represents a sample as opposed to one individual, we used stickers to create a dotplot.  Students took samples, calculated the sample means and wrote each mean on a sticker for the dotplot.  After taking samples of size 5, students repeated the process for samples of size 10.  Students noticed the variability of the dotplot decreased.

Notes

Today marks the start of the second half of the course. There’s a very clear difference in focus from the first half to the second half of the course.  The text was designed to cover all of the high school data analysis and probability standards within the first 5 chapters.  The second half of the course have more of a college-level feel.  We will be spending the next 4 months focusing on statistical significance and testing claims.  Second semester has a really nice flow and consistency.  Students will learn the basics about sampling distributions in chapter 6 and will then continue to use that knowledge and extend it for the rest of the year.  Because of the way the content will build on itself, you will do yourself a huge favor by focusing on getting students to develop a deep understanding of sampling distributions and significance in this chapter.  It’s totally worth taking the extra time now to get it right so that you aren’t fighting misconceptions for the rest of the year.

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