Displaying Quantitative Data with Graphs
Day 4 - Lesson 1.2
Make and interpret dot plots, stemplots, and histograms of quantitative data.
Identify the shape of a distribution from a graph.
Describe the overall pattern (shape, center, and variability) of a distribution and identify any major departures from the pattern (outliers).
Compare distributions of quantitative data using dot plots, stemplots, and histograms.
Activity: How Many Pairs of Shoes Do You Own?
Have students come up to the white board to record the number of pairs of shoes that they own. For the first page of the Activity, students will be using the class data in order to describe a distribution. For the second page of the Activity, they will given a second data set to compare the two distributions.
Students should be somewhat familiar with the applets from www.stapplet.com from Lesson 1.1. Help them to recognize they will be using a different applet today because the data is quantitative, rather than categorical.
This Activity works best by breaking it into two parts. Have students work in pairs or groups to complete the first page, then come back together as a whole class to debrief. Then do the same for the second page of the Activity.
When students are describing the shape of a distribution, encourage them to use -ly adverbs in their description. For example, say “fairly symmetric or slightly skewed right, or later approximately normal). It is very unlikely that any distribution is a perfect symmetric, skewed right, or normal distribution. The -ly word softens up the description to account for this idea.
Students can use the acronym SOCV (shape, outliers, center, variability) to remember the ideas that should be addressed when describing a distribution. If you are using previous versions of The Practice of Statistics, you will notice that the 6th edition has moved from using the more general term of “spread” to the more statistical term of “variability”.
Be sure that students include a key when they make their stem and leaf plot. Question #1 on the 2010B AP Exam asked students to make a stem plot and the rubric called for students losing credit if they forgot to include a key.
AP Exam Tips
It is very common that the first question on the AP Exam will ask students to describe a distribution or compare two distributions based on some graphs (see 2016 #1 or 2015 #1). Here are some very important tips:
According to the rubrics over the years, it is important for students to address shape, center, variability, and outliers in their response.
When comparing two distributions, students should compare shape, center, variability and outliers between the two distributions using comparative words (less than, greater than, similar to). Don’t simply list shape, center, variability, and outliers for each distribution. They must compare.
Students must establish context. They do this by identifying the variable that is being displayed by the graph. “The distribution of Robin’s tip amounts is skewed to the right…”. Context needs to be stated only once in the response. Students do not need to repeat context over and over again.
Check Your Understanding
The second question on the Check Your Understanding has students comparing two distributions using a side-by-side stem plot. Identifying the shape of each distribution can be confusing here (one of the Stats Medics even got this wrong on a final exam in college). The distribution being displayed on the left (resting pulse rates) appears to be skewed left. This is not the case. Most of the pulse rates are in the 60s, 70s, and 80s, but then there are a few values higher up (90, 96, 104, 120), indicating the distribution is skewed right.