Investigations 13 and 14: Drawing a Histogram–The Importance of Binning

One challenge when we draw a histogram is choosing the width for the bins or the number of bins. In Figure 4, for example, the bins for yellow M&Ms are five units wide—the first bin, for example, includes samples with 5, 6, 7, 8, and 9 yellow M&Ms—but the bins are two units wide for all other colors of M&Ms. There are no simple rules for determining the number or the width of bins, so it is a good idea to try several bin sizes before we settle on a final choice.

Investigation 13. The histograms in Figure 5, from left-to-right, use bins widths of 1, 2, and 3 units, respectively. Note that the x-axis shows the specific results gathered into each bin. How does the choice of bin size affect your understanding of this data? Which of these histograms provides the best representation of the data? As part of your answer, identify what you see as the limitations of the other two histograms.

Investigation 14 Draw a histogram for the total number of M&Ms and explain the reason(s) for your choice of bin size. Compare your plots to those in Figure 4 and discuss any similarities and any differences.