Applications of Bar Graphs: Fresh Take

  • Create side-by-side and stacked bar graphs using technology
  • Use side-by-side and stacked bar graphs to compare different groups

Interpreting Side-by-Side and Stacked Bar Graphs

The Main Idea

Side-by-side bar graphs are bar graphs that create two bars in the chart for each group to represent data for two categorical variables from more than one group. Side-by-side bar graphs are most efficient when presenting data counts (not percentages).

Stacked bar graphs also represent data for two categorical variables from more than one group, but stacked rather than side-by-side. Stacked bar graphs are most efficient when presenting percentages of the data in each group (not counts).

The example problem below presents the same data displayed four different ways: as a contingency table (counts), as a conditional distribution (percentages), as side-by-side bar graphs (counts), and as stacked bar graphs (percentages). This won’t always be the case; sometimes a bar graph will display percentages, but these examples represent efficient uses of these displays. Also note that these bars are vertical, but some side-by-side and stacked graphs are displayed horizontally.

The following displays present alcohol consumption by students at a college. Counts are given for four categories (abstaining, light consumption, moderate consumption, and heavy consumption) for first-year, second-year, third-year, and fourth-year students. The Contingency Table shows the level of alcohol consumption self-reported by 253 students. We can see, for example, that of the 95 second-year students who responded, 27 identified themselves as light drinkers.

A contingency table showing the counts of alcohol consumption based on class year.

  1. How many third-year students identified themselves as heavy drinkers?

Now let’s look at the data as percentages rather than counts.

A conditional distribution of alcohol consumption given class year using the same data as the previous table.

Note that the percentages are given in decimal form. Multiply by 100 to convert to percentages. Each row adds up to 1 (100%) of all responses for each class year. We can see that the 27 of 95 second-year students we located in the table above is represented in this table as [latex]\dfrac{27}{95}\approx0.284[/latex], which is about 28.4%.

2. What percentage of third-year students identified themselves as heavy drinkers?

Side-by-Side Bar Graphs

 

A bar graph shows the alcohol consumption by year with different bar colors illustrating abstaining from alcohol, light consumption, moderate consumption, and heavy consumption.

Here, we see the data from the contingency table displayed as side-by-side bar graphs. The horizontal axis contains the four class years of students while the vertical axis indicates the height of each bar in numbers of students. The differently colored bars each represent an alcohol consumption category.

1. Try to locate the 27 second-year students who identified as light drinkers. What color is the bar and where is it located along the horizontal axis?

2. Which class year reports the most moderate drinking?

Stacked Bar Graphs

 

A stacked bar graph of alcohol consumption by year, using the same bar colors and data as the above bar graph.

Finally, we see the information from the conditional distribution displayed as stacked bar graphs.

1. Which class year reported the lowest proportion of heavy drinkers?

2. How did alcohol consumption change from class year to class year?