Bar Graph
Statistics & ProbabilityA bar graph uses rectangular bars to compare the frequencies or values of different categories.
Definition
A bar graph uses bars of different heights to compare amounts in different categories. The taller the bar, the larger the amount.
Example
A bar graph showing the number of students who prefer each sport: Soccer: $12$, Basketball: $9$, Swimming: $5$, Baseball: $7$. Soccer has the tallest bar.
Key Insight
Bar graphs make it easy to compare categories at a glance. The gaps between bars remind us that the categories are separate groups, not a continuous range.
Definition
A bar graph (bar chart) displays categorical data with rectangular bars whose lengths are proportional to the frequencies or values they represent. Bars are separated by spaces to emphasize the distinct nature of categories. Bars can be vertical or horizontal.
Example
A double bar graph compares monthly sales for two products side by side for each month. This lets the viewer compare both products and track trends across months simultaneously.
Key Insight
Bar graphs are for categorical data; histograms are for continuous numerical data. The spaces between bars in a bar graph vs. the touching bars in a histogram signals this distinction.
Definition
A bar graph represents the empirical distribution of a categorical or ordinal variable. Stacked bar graphs partition each bar by a secondary variable, enabling comparison of both absolute and relative frequencies. Mosaic plots generalize stacked bars using area-proportional rectangles for two categorical variables simultaneously.
Example
A stacked $100\%$ bar graph normalizes each bar to $100\%$, showing the relative breakdown across a secondary categorical variable. This highlights compositional differences even when group sizes differ.
Key Insight
Visual perception research (Cleveland and McGill, 1984) ranks bar length as one of the most accurately perceived graphical encodings, making bar graphs superior to pie charts for precise comparisons.