Displaying Quantitative Data: Histograms (Lesson 1.5)
Chapter 1 - Day 6
Make histograms of quantitative data.
Interpret or describe histograms.
Compare distributions of quantitative data with histograms.
Have students get out their phones and estimate how many text messages they sent yesterday. “But what about group chats…do those count?” Absolutely. The number of students with over 100 amazed and surprised us.
Students will use this applet to quickly create a histogram. Be sure that when they are describing the distribution that they address shape, center, variability, and outliers.
Students first learned about frequency tables in Lesson 1.1 as a way to organize data for a categorical variable. But number of text messages is a quantitative variable, so how can we use a frequency table for question #1? Well, the answer is that we took the quantitative variable of number of text messages and turned it into a categorical variable by creating intervals (0-99 text messages, 100-199 text messages…). This way we can collect counts for each interval, which will help us to construct a histogram.
When creating histograms, students often don’t know what to do with a value that is on the edge of an interval. The standard convention in statistics is that a histogram bar includes the value that is the left endpoint and does not include the value that is the right endpoint. For example, one of the bars might include “100 up to but not including 200 text messages."
Be sure to point out that the bars have no space between them for a histogram. Back in Lesson 1.2, students made bar graphs, which did have a space between the bars. The difference is that bar graphs are used for categorical data and histograms are used for quantitative data.
This might be a good time to connect Lessons 1.3, 1.4, and 1.5. All three lessons are dedicated to displaying quantitative data (with dotplots, stemplots, and histograms). Discuss the pros and cons of each. Dotplots and stemplots show us all of the individual values, where a histogram does not….but a histogram might do a better job of displaying the shape of the distribution.
In the end, we should all agree that the dotplot is far superior to all other graphs.