Lesson 11: What Shape Are You In?

Objective:

Students will learn to classify distributions in terms of shape, and can suggest theories for why a distribution might be one shape or another.

Materials:

Sorting Histograms handout (LMR_1.10_Sorting Histograms) - one copy per group of 4 students. (This activity comes from the AIMS project, University of Minnesota, J. Garfield.)
Advanced preparation required (see step 1 below)

Vocabulary:

symmetric left-skewed right-skewed unimodal bimodal

Essential Concepts:

Identifying the shape of a histogram is part of the interpret step of the Data Cycle.

Lesson:

Distribute the cutouts from the Sorting Histograms handout (LMR_1.10). Give each student team all of the 24 histograms (can be paper clipped together or put in small zippered bags).

Advanced preparation required: Print the Sorting Histograms file (LMR_1.10). Cut each histogram so that it is on its own piece of paper. Create enough sets for each team to have all 24 histograms. They can be paper clipped together, or put in small zippered bags.

LMR_1.10
Inform students that the type of data being measured is indicated on the horizontal axis, and the vertical axis represents how many observations are in each bar.
The students will then sort their stack of plots into different piles according to their shapes. Histograms that have similar shapes should be sorted into the same stack.
Once the student teams have agreed upon the histogram shape groupings, they should discuss and write down answers to the following in their DS journals:
1. Describe what’s similar about the plots in each group. Answers will vary, but should be grouped by the overall shape of the distribution. For example, plots with a higher density of bars on the right side of the plot should all be in the same group.
2. Pick one graph in each group that is the best example of that group. Answers will vary.
3. Give the group a name that you think describes the general shape. Answers will vary.
4. If there are graphs that do not fit into any group, try to determine why it was impossible to place them. What is different or confusing about them? Answers will vary.
After each team has had time to discuss and write down their observations, have a class discussion about the histogram groupings. Do the students agree about the general shapes?
In statistics, we use specific terminology when discussing the shapes of distributions, such as symmetric, right-skewed, left-skewed, unimodal, bimodal, etc. Did any of the teams use these terms? If not, introduce each one and ask which of the 24 histograms could be classified as that shape.
Next, introduce the following scenarios and ask students to determine what a corresponding histogram might look like. They should use statistical terms to describe their answer.
1. The grades on an easy test. Left-skewed, unimodal
2. The grades on a difficult test. Right-skewed, unimodal
3. The number of times IDS students study during the first week of class. Answers will vary.
4. The age of cars on a used car lot. Right-skewed, probably unimodal
5. The amount of time spent by students on a difficult test (max time allowed is 50 mins). Left-skewed, but may also just be one bar with all observations at 50 mins, unimodal
6. The heights of students in your high school band. Symmetric, bimodal
7. The salaries of all persons employed at the Los Angeles Unified School District. Right-skewed, potentially bimodal (teachers vs. LAUSD administrators)

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework

Students should continue to collect nutritional facts data using the Food Habits Participatory Sensing campaign on their smart devices or via web browser.