Density Curves and the Normal Distribution (Lesson 2.3)
Chapter 2 - Day 3
Learning Targets
-
Use a density curve to model a distribution of quantitative data.
-
Identify the relative locations of the mean and median of a distribution from a density curve.
-
Draw a normal curve to model a distribution of quantitative data.
Experience First
Before class starts, you will need to have three stations set up:
-
Table with a bunch of dice
-
Table with pennies. On the ground there is a target set up about 100 cm away from the tossing line.
-
Table with stopwatches. If you don’t have access to stopwatches, students can use the stopwatch on their phones.
Tips for making data collection more efficient:
-
Assign groups to different stations, then rotate them.
-
The penny toss takes the longest amount of time. Consider making two or three targets and tossing lines.
-
Have one or two computers at each station, with this spreadsheet open.
-
On your teacher computer, have the spreadsheet open, as well as three tabs in a browser, each one using the 1 Quantitative Variable, Single Group applet. You can preload the variable names (Die Roll, Distance from target, Stopwatch time).
Formalize Later
Use the 1 Quantitative Variable, Single Group applet to reveal the actual histogram (and mean and median) for the class data for each task. This is the point at which you introduce the idea of a density curve as a good way to show the shape seen in a histogram.
If the data sets from your class data collection do not give you the intended shape (Task 1: Uniform, Task 2: skewed right, Task 3: approximately Normal), you can always use our data from a few years back.
For the Lesson App 2.3, students might struggle with question 1. Consider doing this question as a whole class and then releasing them to their groups to finish the remaining questions.