In Topics B and C, students study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution. The mean and mean absolute deviation (MAD) are used for data distributions that are approximately symmetric, and the median and interquartile range (IQR) are used for distributions that are skewed. Students apply their experience in writing, reading, and evaluating expressions in which letters stand for numbers (6.EE.A.2) as they learn to compute and interpret two pairs of statistical measures for center and spread (6.SP.A.5).
In Topic C, students study median as a measure of center and interquartile range as a measure of variability. Students learn that these measures are preferred when the shape of the distribution is skewed. Students develop in Topic B, and reinforce in Topic C, the idea that a measure of center provides a summary of all its values in a single number, while a measure of variation describes how values vary, also with a single number (6.SP.A.3).
Measures of center and variability for distributions that are approximately symmetric (mean and MAD) are covered before measures (median and IQR) for skewed data distributions. This choice was made because it is easier for students to understand measuring center and variability in the context of symmetric distributions.
For students, box plots are the most difficult of the graphical displays covered in this module. This is because they differ from dot plots and histograms in that they are not really a display of the data but rather a graph of five summary measures (minimum, lower quartile, median, upper quartile, and maximum). This graph conveys information on center and variability but is more difficult for students to interpret because, unlike histograms, where large area corresponds to many observations, in a box plot, large area indicates spread and small area indicates a large number of observations in a small interval. Box plots also require the calculation of quartiles and are best covered after quartiles have been introduced and used to calculate the IQR. For these reasons, box plots are introduced late in the module after the IQR and after students have already developed some fundamental understanding of data distributions, which is easier to do in the context of dot plots and histograms.