Common Core Standards: Math
4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
In the beginning, there were statistical questions. Those questions brought forth varying data from the earth, which students summarized using measures of center and spread. They recognized and understood and calculated; they were merry; and it was good.
But then comes the horrible word, "Display," and cramps our style. Why? Well, it requires students to do a lot more than just recognize or understand; it means students have to take data in numerical form and express it in a totally different form—namely, they've got to create dot plots, histograms, and box plots.
Thankfully, they're all variations on a theme: the number line.
We recommend starting with dot plots, helping students realize that it's essentially a number line with dots stacked on top of each other to indicate frequency. In other words, students should understand that if we've got twenty data points, there should be twenty dots on the graph. Dot plots are probably the most intuitive of the bunch, and they're great for students to develop a holistic understanding of center, spread, and shape.
For values that are better sorted into ranges than discrete values, students should use histograms to display their data. While we lose of the some of the details of the individual data points in histograms, we gain a better understanding of the shape of the data. Remind students to follow the cardinal rules of histograms: the bars of a histogram must (1) be the same width, (2) touch each other, and (3) include the lower limit's value and not the higher limit's value. Students should also be able to make histograms using frequencies or relative frequencies on the vertical axis.
Finally, students should know that creating a box plot (a.k.a. the box-and-whisker plot) requires more than putting Mrs. Whiskerson in a shoebox. Once they're comfortable with the median and the interquartile range, it shouldn't be too much of a stretch to convert the data into boxes on the number line. Don't worry about outliers, though; leave that for their high school stats teachers.