Double Bar Graphs and Many-to-One Correspondence
Double bar graphs display two data sets side by side for each category, enabling direct comparison. A city might compare rainfall in 2024 and 2025 for each month: 12 categories, 2 bars per category. The many-to-one scale is essential for real data: monthly rainfall in millimetres requires a scale of 1 unit = 5 or 10 mm or the graph would be enormous. Reading double bar graphs requires all the skills of single bar graphs plus the ability to compare between bars within each category.
Double bar graphs
Two bars per category, each a different colour representing a different data set. A legend (key) identifies which colour represents which data set. The bars share the same scale and axis. To compare: look at both bars in the same category. Which is taller? By how much? To summarize: which data set consistently had higher values across categories?
Scale selection for double bar graphs
With two data sets, the scale must accommodate the maximum value in EITHER set. If rainfall ranged from 20 to 140 mm in one year and 15 to 160 mm in the other, the scale must reach at least 160. Choose a scale that makes the tallest bar 8-12 units: scale of 1=15 makes 160mm approximately 11 units. Consistent scale across both data sets is essential for valid comparison.
Comparative interpretation
A double bar graph comparing school library book loans in Grade 4 and Grade 5 by genre. Level 1 question: how many fiction books did Grade 4 borrow? Level 2: how many more fiction books did Grade 5 borrow than Grade 4? Level 3: overall, which grade borrowed more books? Which genre showed the biggest difference between grades? These are the questions that make data meaningful.