Describing Density Curves, Normal Distributions,
The 68–95–99.7 Rule
Chapter 2 - Day 4 - Lesson 2.2
Use a density curve to model distributions of quantitative data.
Identify the relative locations of the mean and median of a distribution from a density curve.
Use the 68–95–99.7 rule to estimate (i) the proportion of values in a specified interval, or (ii) the value that corresponds to a given percentile in a Normal distribution.
Activity: Exploring Density Curves
Today we will begin exploring density curves. The idea for this came from Elizabeth DeCarli and Andres Marti from SFUSD. We attended their session at the NCTM annual conference last year and it was fantastic!
We are going to conduct three different experiments in order to collect data:
Roll a die 3 times. Record the rolls.
Toss a penny at a target and measure and record the distance the penny lands from the target.
Use the stopwatch on your phone and try to stop it on exactly 5 seconds. Record the time you stopped on.
Preparing for Inference
The most important part of this process is for students to predict what they think the graphs of these data will look like if we do this many, many times and where the mean and median would be located. After students have completed the experiments, they should submit their data into a google spreadsheet. When the groups are finished, copy the data for each experiment and paste it into this applet. Use the graphs of the data to create density curves for each experiment. Mark where the mean and median are located.
The data from the stopwatch experiment should be approximately Normal. We’ll use this to segue into Normal curves and the 68-95-99.7 rule. Share the rule with the class by labeling the blank Normal curve. Students can work in their groups to answer the questions about the Normal curve. Go over the answers with the class.
You could also make a Normal Curve flipbook to share the 68-95-99.7 rule. But if you do, you will not be able to complete this whole lesson in an hour. This could be done the next day with practice problems if you like.
You should set up the penny tossing station before class. We measured the target 1 meter from the start point. This worked well. Students could get pretty close to the target without it being too easy. We had no problem getting a right skewed distribution.
This is a very full day! It will be challenging to get through everything in one hour. We had each student do every experiment. Instead, assign each group one of the three experiments. This would save a lot of time.