Describing Location in a Distribution (Lesson 2.1)
Chapter 2 - Day 1
Find and interpret a percentile in a distribution of quantitative data.
Find and interpret a standardized score (z-score) in a distribution of quantitative data.
Use percentiles or standardized scores (z-scores) to compare the location of values in different distributions.
First of all, let’s take care of the movie reference. If you don’t know, you’re not thinking fourth dimensionally. It’s the most perfect blockbuster ever made.
This Activity is a perfect example of how the EFFL teaching philosophy is different than some other more traditional teaching models. Instead of starting the lesson with the teacher providing a definition of percentile and a formula to calculate a z-score, students are working in small groups to discover each of these ideas. After the students have the experience of thinking and discussing these concepts in groups, the teacher formalizes the learning with definitions and formulas.
As you are monitoring group work, focus in on question #4. Consider asking students “How did you get 17?” and “Mathematically, what did you do to get 1.7?” You might even ask students “Could you come up with a formula for calculating the number of standard deviations away from the mean?”
Notice that the z-score formula that is presented during the debrief of the activity does not have any fancy Greek notation. Also, we used “score” in the formula here to match the context of the activity. You will notice that we changed this to a more general “value” in the QuickNotes.
During the QuickNotes, ask for a student volunteer to give the words that should be included for the interpretation of the z-score. For the student that volunteers, consider making this their full-time job.
The z-score calculation and interpretation are absolutely critical building blocks for this course. Very soon, students will be using z-scores to find area under normal distributions, which later in the course will become a test statistic for a significance test. One of the very nice things about how this course is organized is that students will get a lot of spiraled practice with all of this.