Side-by-side boxplots in AP Statistics

Side-by-side boxplots display two or more boxplots on the same numeric scale (stacked vertically or horizontally) so you can directly compare the distributions of independent groups by center, variability, and outliers, the core skill of AP Stats Topic 1.9.

Verified for the 2027 AP Statistics examLast updated June 2026

What are side-by-side boxplots?

Side-by-side boxplots are exactly what they sound like. You take a boxplot for each group (say, recovery times for Treatment A and Treatment B) and line them up on the same axis. Because every box sits on one shared scale, your eye can instantly compare medians, IQRs, ranges, and flagged outliers across groups. One boxplot describes a distribution; side-by-side boxplots compare distributions.

In the CED, this lives in Topic 1.9 (Comparing Distributions of a Quantitative Variable). The essential knowledge says any graphical representation, including histograms or side-by-side boxplots, can compare two or more independent samples on center, variability, clusters, gaps, outliers, and other features. One honest limitation to know is that boxplots only show the five-number summary, so they hide shape details like gaps, multiple peaks, and clusters that a histogram or dotplot would reveal.

Why side-by-side boxplots matter in AP® Statistics

This term supports learning objectives 1.9.A (compare graphical representations for multiple sets of quantitative data) and 1.9.B (compare summary statistics for multiple sets) in Unit 1: Exploring One-Variable Data. Side-by-side boxplots are arguably the single most common comparison graph on AP Stats free-response questions, and the skill they unlock, writing a real comparison using comparative language about center, spread, shape, and outliers in context, follows you through the entire course. When you reach inference for two means or two medians later in the course, the first move is almost always to look at side-by-side boxplots of the sample data. Head to the Topic 1.9 study guide for the full comparing-distributions playbook.

How side-by-side boxplots connect across the course

Box Plot (Unit 1)

A single boxplot is the building block here. It encodes the five-number summary (min, Q1, median, Q3, max) plus outliers. Side-by-side boxplots are just multiple of these on one shared scale, which turns a description tool into a comparison tool.

Median (Unit 1)

The line inside each box is the median, so side-by-side boxplots make comparing centers trivial. When distributions are skewed or have outliers, the median is the resistant measure of center you should compare, and boxplots hand it to you visually.

Skewness (Unit 1)

You can read rough shape off each box. A longer whisker and a stretched half-box on the right side suggest a distribution skewed to the right. Just remember a boxplot can't show gaps or two peaks, so 'roughly symmetric' from a boxplot is a softer claim than from a histogram.

Stem-and-Leaf Plot (Unit 1)

A back-to-back stemplot is the other classic two-group comparison graph. It keeps every individual data value (so you can see clusters and gaps), while side-by-side boxplots trade that detail for a cleaner summary that scales easily to three or more groups.

Are side-by-side boxplots on the AP® Statistics exam?

Multiple-choice questions tend to hand you a research scenario, like comparing recovery times for two treatments or heights of male and female students, and ask which graphical and numerical summaries are most appropriate. Side-by-side boxplots paired with five-number summaries (or medians and IQRs) is the classic correct answer when the goal is comparing center and spread across groups. Watch for distractor stems where the goal is showing counts in intervals for one group; that calls for a histogram, not boxplots. On the free response, you'll often be given side-by-side boxplots and asked to compare the distributions. Full credit requires comparative language ("the median for Group A is higher than for Group B"), addressing center AND variability (shape and outliers when visible), and tying everything to context. Listing facts about each group separately, without comparison words, loses points.

Side-by-side boxplots vs Segmented bar graphs

Both put multiple groups on one display, but they handle completely different data types. Side-by-side boxplots compare a quantitative variable (like test scores) across groups, while segmented or side-by-side bar graphs compare a categorical variable (like favorite subject) across groups. Quick check before you answer an MCQ: if the variable is measured in numbers with units, think boxplots; if it's categories with counts or proportions, think bar graphs.

Key things to remember about side-by-side boxplots

  • Side-by-side boxplots show two or more boxplots on the same scale so you can compare distributions of a quantitative variable across independent groups.

  • They make it easy to compare medians (center), IQRs and ranges (variability), and outliers at a glance, which is exactly what LOs 1.9.A and 1.9.B ask for.

  • Boxplots hide shape details like gaps, clusters, and multiple peaks, so a histogram or dotplot is better when those features matter.

  • When comparing distributions on an FRQ, use explicit comparative language like 'greater than' or 'more spread out,' and always mention context.

  • Because boxplots are built from the five-number summary, pair them with median and IQR (not mean and standard deviation) when distributions are skewed or have outliers.

Frequently asked questions about side-by-side boxplots

What are side-by-side boxplots in AP Stats?

They're two or more boxplots drawn on the same numeric scale so you can compare distributions of a quantitative variable across groups. The CED lists them in Topic 1.9 as a standard tool for comparing independent samples on center, variability, and outliers.

Do side-by-side boxplots show the shape of a distribution?

Only roughly. You can infer skewness from uneven whiskers and box halves, but boxplots cannot show gaps, clusters, or multiple peaks because they only display the five-number summary. If shape details matter, a histogram or dotplot is the better choice.

How are side-by-side boxplots different from a histogram?

A histogram shows how many values fall in each interval for one distribution, while side-by-side boxplots summarize and compare several distributions at once using five-number summaries. On MCQs, a question about displaying counts in 10-point intervals points to a histogram; a question about comparing center and spread across two classes points to side-by-side boxplots.

What statistics should I report with side-by-side boxplots?

Use the measures the plot is built from, meaning the median for center and the IQR (or range) for variability. Mean and standard deviation aren't shown on a boxplot and aren't resistant to the skewness and outliers that boxplots often reveal.

Is comparing side-by-side boxplots on the AP Stats exam?

Yes. Comparing distributions is a staple FRQ task, and side-by-side boxplots are one of the most common displays used. Graders look for comparative language covering center, variability, and outliers, all stated in the context of the data.