Constructing and Comparing Double Displays
Grade 9 students in California Reveal Math Algebra 1 learn to construct and compare double displays — double histograms and double box plots — using identical axis scales to ensure valid visual comparisons. Both histograms must use the same bin width and identical x- and y-axis scales. Both box plots must float over the exact same number line. A common error is the scale trap: using different scales makes one dataset appear wider or taller than it really is, creating misleading comparisons. For example, Dataset X with median 0.45s and IQR 0.10 versus Dataset Y with median 0.52s and IQR 0.25 must share one number line to reveal the true differences.
Key Concepts
Property To visually compare two different data sets, you must construct their graphs side by side or stacked, using identical axis scales . Double Histograms: When comparing two histograms, you must use the exact same bin width ($w$) and the same numerical scale on both the horizontal (x axis) and vertical (y axis) axes. Double Box Plots: Draw both box and whisker plots floating parallel to each other over the exact same horizontal number line.
Examples The Scale Trap (Histograms): Class A scores range from 50–100. Class B ranges from 55–98. Both histograms MUST use the same bins (e.g., width of 10 starting at 50). If you use a bin width of 10 for Class A and 5 for Class B, Class B's data will falsely appear much more spread out than it actually is. The Scale Trap (Vertical Axis): Class A and B both have 30 students. If Class A's tallest bar reaches 12, both y axes must be scaled to at least 12. If Class B's axis stops at 6, its bars will physically look twice as tall as Class A's, creating a misleading visual comparison. Comparing Double Box Plots: Dataset X has a median of 0.45 seconds and an IQR of 0.10. Dataset Y has a median of 0.52 seconds and an IQR of 0.25. When drawn on the same number line, you can instantly see that Group X not only has a faster (lower) center but is also much more consistent (shorter box).
Common Questions
What rule must both histograms follow when creating a double display?
Both histograms must use the exact same bin width and identical numerical scales on both the horizontal and vertical axes. Different scales create false visual impressions.
What rule must double box plots follow?
Both box plots must be drawn floating over the exact same horizontal number line. This ensures any visual size differences reflect real statistical differences.
What is the scale trap in double displays?
The scale trap occurs when two graphs use different scales. A small spread on a zoomed-in graph can look wider than a large spread on a zoomed-out graph, leading to false comparisons.
How can a different y-axis scale mislead in double histograms?
If Class A and Class B each have 30 students but Class A's y-axis goes to 12 and Class B's only to 6, Class B's bars will look twice as tall, falsely implying its data is more concentrated.
What can you compare from double box plots with the same scale?
You can compare centers (median positions), spread (IQR and whisker widths), and overall distribution. Dataset X with IQR 0.10 is clearly more consistent than Dataset Y with IQR 0.25 when drawn on the same axis.
Which unit covers double displays in Algebra 1?
This skill is from Unit 11: Statistics in California Reveal Math Algebra 1, Grade 9.