Describing Quantitative Data Day 2 (Topics 1.81.9)
Chapter 1  Day 8
Learning Targets

Identify outliers using the 1.5×IQR rule.

Make and interpret boxplots of quantitative data.

Use boxplots and numerical summaries to compare distributions of quantitative data.
Activity: Where Do I Stand?
Prepare a dotplot on the board. Use the same values and scale as the one in the Activity (click image to display on your whiteboard…we made this image using this website).
After students have recorded their heights on the dotplot, they are asked to line up in the front of the room, from shortest to tallest. Ask students the following questions:

What height is the median height? Students will likely use the “cross off” method where they start on the ends and work their way to the middle. Once the median is identified, split the line into two groups.

What percent of the data is in each group?

What is the first quartile? What is the third quartile? Use these values to split the line now into four groups.

What percent of the data is in each group?

Identify and record the minimum, first quartile, median, third quartile, and maximum.
This part of the Activity shows students the purpose of a boxplot is to visually show the data split into quarters.
Teaching Tip: Finding the Quartiles
Most students will be familiar with the process for finding a median.

If the total number of data values is odd, the median is the middle value.

If the total number of data values is even, the median is the average of the two middle values.
When it comes to finding the Q1 and Q3, students often wonder whether or not to include the median as part of the lower half of the data, the upper half of the data, or neither. While there is no correct answer here, the convention for AP Statistics (and your TI 83/84 calculator) is:

If the total number of data values is odd, the median is the middle value. Do notinclude the median as a data value in the lower half or the upper half of the data.

If the total number of data values is even, the median is the average of the two middle values. The left middle value is part of the lower half of the data. The right middle value is part of the upper half of the data.
Teaching Tip: Outliers
There are many different criteria that can be used to determine whether a data value is an outlier (all of them are ultimately subjective). For AP Stats, we use the following to identify what we call values that are “way too small” or “way too big”:
way too small < Q1 – 1.5IQR
way too big > Q3 + 1.5IQR
Teaching Tip: Modified Boxplot vs Boxplot
Many students will learn in middle school that a “modified box” plot will show outliers as a special character (star or * or a blue dot).
When John Tukey invented the boxplot in 1970, he used the above version (with outliers shown as distinct points). So, in reality, this is not a “modified” box plot…it is the “OG boxplot”. Any boxplot students encounter in AP Statistics will be in this form. In other words, if students see a boxplot that does not show a distinct outlier, they can assume there is no outlier in the data set (according to the “way too small, way too large” rule above).