Side-by-side bar graphs in AP Statistics

A side-by-side bar graph displays the distribution of one categorical variable broken down by the categories of another, placing bars for each group next to each other so you can compare distributions and check for association (AP Stats Topic 2.2, UNC-1.P.1).

Verified for the 2027 AP Statistics examLast updated June 2026

What is Side-by-side bar graphs?

A side-by-side bar graph (also called a grouped bar graph) shows two categorical variables at once. You take one categorical variable, like exercise frequency, and draw a separate bar for each category of a second variable, like age group. The bars for each group sit right next to each other, so your eye can jump across and compare. Per the CED (UNC-1.P.1), it's one of three standard displays for two categorical variables, alongside segmented bar graphs and mosaic plots.

The data behind a side-by-side bar graph usually comes from a two-way table (contingency table), where each cell holds a frequency count or relative frequency. The graph is basically that table drawn as bars. One important choice you control is whether the bars show counts or relative frequencies. If the groups have different sizes, counts can be misleading, so relative frequencies (proportions within each group) are the fair comparison. If the bar patterns look different from group to group, that's visual evidence the two variables are associated.

Why Side-by-side bar graphs matters in AP Statistics

This term lives in Topic 2.2 (Representing Two Categorical Variables) in Unit 2: Exploring Two-Variable Data, supporting learning objective 2.2.A: compare numerical and graphical representations for two categorical variables. The bigger idea is association. Unit 2 is all about asking whether two variables are related, and side-by-side bar graphs are the categorical-variable version of that question. If the distribution of one variable looks roughly the same across every group, the variables are probably independent. If the shapes differ, they're associated. That same logic comes back later in inference when you run a chi-square test for association, so reading these graphs correctly now pays off in Unit 8.

How Side-by-side bar graphs connects across the course

Bar graph (Unit 1)

A side-by-side bar graph is just a regular one-variable bar graph repeated for each group of a second variable. If you can read a bar graph from Unit 1, you can read this; you're just comparing several of them at once.

Marginal Relative Frequencies (Unit 2)

The two-way table that feeds a side-by-side bar graph also gives you marginal and conditional relative frequencies. The bars within one group are literally the conditional distribution of that group drawn as a picture.

Simpson's Paradox (Unit 2)

Breaking data down by a second categorical variable, which is exactly what side-by-side bar graphs do, is how you catch Simpson's Paradox. A trend visible in the combined data can reverse once you split by groups.

Bivariate Data (Unit 2)

Side-by-side bar graphs are the categorical-categorical corner of bivariate data. Scatterplots handle two quantitative variables; this graph handles two categorical ones. Same question (are these variables associated?), different tools.

Is Side-by-side bar graphs on the AP Statistics exam?

Multiple-choice questions usually test whether you can pick the right display for a situation. A classic stem asks which graph best shows the distribution of one categorical variable across different groups, and side-by-side bar graphs are often the answer when the goal is comparing counts within categories. You should also be ready for the reverse, where a mosaic plot or segmented bar graph beats a side-by-side display because group sizes differ and proportions matter more than counts (a Fiveable practice question on exercise habits by age group tests exactly this trade-off). On FRQs, you're more likely to interpret one of these graphs than draw one. The move the exam rewards is comparing distributions across groups in context and stating whether the graph suggests the variables are associated. Always say whether the bars represent counts or relative frequencies before you compare.

Side-by-side bar graphs vs Segmented bar graphs

Both display two categorical variables, but side-by-side bar graphs place separate bars next to each other (good for comparing actual counts across categories), while segmented bar graphs stack the categories into one bar per group that totals 100% (good for comparing proportions). If group sizes differ a lot, a segmented bar graph or mosaic plot makes the proportional comparison clearer; a side-by-side graph of raw counts can make a big group look dominant just because it's big.

Key things to remember about Side-by-side bar graphs

  • A side-by-side bar graph shows one categorical variable broken down by the categories of another, with bars for each group placed next to each other.

  • It's one of three CED-listed displays for two categorical variables, along with segmented bar graphs and mosaic plots (UNC-1.P.1).

  • The data comes from a two-way (contingency) table, and the bars can represent either frequency counts or relative frequencies.

  • If the bar patterns differ noticeably from group to group, that's graphical evidence the two variables are associated.

  • When groups have different sizes, use relative frequencies instead of counts, or the bigger group will dominate the graph for no meaningful reason.

  • Side-by-side bar graphs excel at comparing counts within categories; segmented bar graphs and mosaic plots excel at comparing proportions.

Frequently asked questions about Side-by-side bar graphs

What is a side-by-side bar graph in AP Stats?

It's a graph that displays one categorical variable broken down by the categories of another, with bars for each group placed next to each other. It's used in Topic 2.2 to compare distributions and check whether two categorical variables are associated.

What's the difference between a side-by-side bar graph and a segmented bar graph?

Side-by-side graphs put separate bars next to each other, which makes raw counts easy to compare. Segmented bar graphs stack the categories into one bar per group, usually scaled to 100%, which makes proportions easy to compare. Both summarize the same two-way table.

Do side-by-side bar graphs show association between variables?

They can show evidence of association, yes. If the distribution of one variable looks different across the groups of the other, the variables appear associated. But a graph alone never proves causation; that requires a randomized experiment.

Should a side-by-side bar graph use counts or percentages?

Counts work fine when groups are similar in size. When group sizes differ, use relative frequencies (percentages within each group), or the comparison gets distorted by group size rather than reflecting the actual relationship.

Is a side-by-side bar graph the same as a histogram?

No. Histograms display quantitative data with bars that touch, while bar graphs (including side-by-side ones) display categorical data with gaps between bars. Mixing these up is a classic AP Stats error worth avoiding on the exam.