Exercises: Layout, Composition, and Small Multiples

These exercises are non-programming. They build the mental discipline of composition — arranging multiple charts on a page as a deliberate design act rather than an afterthought. Do them with a sketchbook and pencil, or with a whiteboard and marker. Physical sketching forces decisions that screen mockups often obscure.

Part A: Conceptual (7 problems)

A.1 ★☆☆ | Recall

Define "composition" in the sense used in this chapter. What is the difference between a collection of well-designed individual charts and a well-composed multi-chart figure?

Guidance Composition is the arrangement of visual elements into a coherent whole. A collection of good charts laid out poorly is still a poor figure, because composition does work that no individual chart can do on its own: enabling comparison, establishing hierarchy, guiding reading order, creating visual unity. Your answer should name at least some of these jobs.

A.2 ★☆☆ | Recall

Name the four "jobs of composition" introduced in Section 8.1 and describe what each one means in your own words.

Guidance The four are: enabling comparison, establishing hierarchy, guiding reading order, and creating visual unity. For each, describe what goes wrong when the job is not done well. Comparison fails when panels use different scales. Hierarchy fails when every panel looks equally important. Reading order fails when the panel sequence does not match the argument. Visual unity fails when the figure looks like a collage of unrelated images.

A.3 ★★☆ | Understand

Explain the Gestalt principle of alignment and describe a specific way it should be applied to a two-panel time-series figure.

Guidance Alignment says that elements sharing a common edge are perceived as organized and related. For two time-series panels, the key alignment is a shared x-axis: the same time range, the same tick positions, with the plotting-area left and right edges aligned between panels. This alignment enables comparison at matching x-positions without mental computation. Pixel-level alignment matters — a two-pixel mismatch is visible as "something is slightly off."

A.4 ★★☆ | Understand

The chapter defines a small multiple as a "set of charts that share the same visual encoding." Why is shared encoding essential? What happens when you have multiple panels with different chart types in what looks like a small-multiple layout?

Guidance Small multiples work because the reader can compare across panels without having to re-learn how to read each panel. The shared encoding means the visual grammar is identical — same axes, same scales, same chart type — so only the data varies. Mixing chart types in the same layout defeats the comparison: the reader has to process each chart separately and cannot see differences "pre-attentively." The result is a dashboard (different chart types for different questions), not a small multiple.

A.5 ★★☆ | Analyze

Cleveland's "banking to 45 degrees" rule for time-series aspect ratios says that the average slope of the line segments should be around 45 degrees. Explain the perceptual reasoning behind the rule. Why 45 degrees and not 30 or 60?

Guidance Human perception is most accurate at distinguishing slope differences near 45 degrees. Slopes that are too shallow (close to horizontal) look the same even when they are meaningfully different. Slopes that are too steep (close to vertical) also look the same — they all look "steep." The 45-degree region is where small slope differences remain perceptible. The rule is a perceptual finding, not a mathematical necessity, but it has held up under experimental scrutiny.

A.6 ★★☆ | Analyze

The chapter describes the Z-pattern for reader scanning of multi-panel figures. Explain how the Z-pattern should inform hero placement. What goes wrong if the hero panel is placed in the bottom-right?

Guidance The Z-pattern says the eye lands at the top-left, scans to the top-right, drops diagonally to the bottom-left, and ends at the bottom-right. The top-left is where the reader's freshest attention lands. A hero panel placed in the bottom-right is read last, after the reader's attention has already been distributed across the other panels — it gets the leftover attention. Placing the hero in the top-left aligns the composition with the reader's natural scanning pattern and maximizes the attention the hero receives.

A.7 ★★★ | Evaluate

Compare and contrast small multiples and dashboards. Give a specific scenario where each is the right choice, and explain why the alternative would not work.

Guidance Small multiples: same chart type across different data slices. Use when comparing the same relationship across many groups — e.g., "COVID case trajectories across 50 U.S. states" as 50 small line charts. Dashboards: different chart types across different aspects of a system. Use when monitoring multiple kinds of questions about the same thing — e.g., "hospital operations dashboard" with a line chart of admissions, a bar chart of staffing, a table of key indicators, and a map of patient origins. Swapping them fails: a dashboard of 50 line charts is cluttered and hides the comparison; a small multiple of 5 different chart types is incoherent and impossible to compare.

Part B: Applied — Layout and Design (10 problems)

B.1 ★★☆ | Apply

You have six charts showing: (1) monthly revenue for 2024, (2) regional breakdown of revenue, (3) top 10 products by unit sales, (4) customer churn rate over time, (5) net promoter score trend, (6) cost of goods sold by quarter. Sketch a composition for these six charts as a business dashboard. Identify which chart is the hero, where each panel goes in the layout, and how you would enforce visual unity across the different chart types.

Guidance Revenue over time is probably the hero — it is usually the most-monitored metric. Place it in the top-left, larger than the others. Related supporting charts (regional breakdown, top products) go nearby. Secondary metrics (churn, NPS, COGS) can go in a second row. Visual unity: consistent typography, a single accent color used across panels, aligned margins, consistent tick formatting.

B.2 ★★☆ | Apply

You need to compare vaccination rates over time across 20 countries. Sketch a small-multiple layout for this data. How many panels do you use? What order do you put them in? What goes on the shared axes? What (if anything) differs across panels?

Guidance 20 panels in a 4×5 or 5×4 grid. Each panel is a small line chart of vaccination rate over time. Shared x-axis (time range). Consider: shared y-axis (0-100%) so the scale is comparable, OR free y-axis if you want to see the *shape* of each trajectory regardless of absolute level. Ordering: by current rate (highest to lowest) usually makes a ranking visible. Panel labels: country names. Only the data differs across panels; chart type, design, and scales (probably) stay the same.

B.3 ★★☆ | Apply

The chapter recommends wide aspect ratios for time series, square for scatter plots, and tall for ranked bar charts. For each of the following charts, state the recommended aspect ratio and justify it:

  • (a) A 150-year time series of global temperature anomalies
  • (b) A scatter plot of GDP per capita vs. vaccination coverage for 190 countries
  • (c) A horizontal bar chart ranking the 50 U.S. states by 2024 population
  • (d) A short-term time series of stock prices over 30 days
Guidance (a) Very wide (maybe 4:1 or 5:1) because 150 years is a lot of horizontal extent and you want to see the full temporal pattern; also apply Cleveland's 45-degree rule. (b) Roughly square (1:1), because scatter plots treat both axes symmetrically. (c) Tall (maybe 1:2), because 50 categories need 50 rows of readable width. (d) Closer to square or slightly wide (3:2) because 30 days is a short time range and a very wide chart would feel empty.

B.4 ★★☆ | Apply

Sketch the climate figure described in Section 8.7 — the three-panel small multiple of temperature, CO2, and sea level from 1880 to 2024. Be explicit about: (a) the aspect ratio of each panel and of the whole figure, (b) what goes on the x-axis and y-axis of each panel, (c) the order of the panels (top to bottom), (d) the shared elements, (e) the differentiating elements.

Guidance Each panel is a wide line chart (maybe 4:1). The whole figure is three panels stacked vertically, so the aspect ratio is roughly 4:3 (wide) × 3 tall = 4:9, which is tall. X-axis on every panel: year (1880-2024). Y-axis: panel 1 is temperature anomaly (°C), panel 2 is CO2 (ppm), panel 3 is sea level (mm). Shared: x-axis, typography, figure title, source attribution. Differentiating: the data, the y-axis labels, possibly the line color.

B.5 ★★☆ | Analyze

You are reviewing a colleague's draft dashboard. It has eight panels: revenue trend, regional breakdown, top products, customer churn, NPS, COGS, a pie chart of expenses, and a 3D bar chart of inventory turnover. The panels are arranged in a 4×2 grid with each panel the same size. Identify three specific compositional problems and propose fixes.

Guidance Problem 1: every panel is the same size, so there is no hierarchy — the reader does not know which chart is most important. Fix: make revenue trend (the hero) larger. Problem 2: the pie chart and 3D bar chart violate the declutter principles from Chapter 6 and the honest-encoding principles from Chapter 4. Fix: replace both with horizontal bar charts. Problem 3: the 4×2 grid with uniform spacing does not group related charts — revenue and regional breakdown probably belong together, churn and NPS belong together. Fix: adjust proximity to reflect logical groupings.

B.6 ★★☆ | Apply

A colleague proposes visualizing "growth in 12 different markets" as a single line chart with 12 overlapping lines (a "spaghetti chart"). Critique this proposal and suggest a specific alternative. Be concrete about the alternative's layout.

Guidance Critique: spaghetti charts with 12+ lines are usually unreadable — the reader cannot follow any individual series or compare between them. The default perceptual response is "a tangle." Alternative: a 3×4 small multiple with one panel per market, shared axes, consistent design. Each panel is a clean single-line chart. The reader can scan across panels to compare growth rates and spot outliers. Ordering: by current size of market, by growth rate, or by geography.

B.7 ★★☆ | Apply

Sketch a "hero plus supporting" layout for a quarterly business review. The hero chart is quarterly revenue over the past 12 quarters. The supporting charts are: regional breakdown, top products, and customer satisfaction trend. Describe the layout including relative sizes, positions, and any alignment decisions.

Guidance One layout: the hero revenue chart occupies the top half of the figure, full width. The three supporting charts occupy the bottom half in a 1×3 grid. All four panels share a consistent design (same typography, same color palette, same time-axis formatting). The hero is larger and visually dominant; the supporting charts are smaller and equally weighted among themselves. The reader's eye lands on the hero first, then scans the supporting row.

B.8 ★★★ | Analyze

Take a published multi-panel figure from a scientific paper, news article, or business report. Evaluate it against the four jobs of composition: does it enable comparison, establish hierarchy, guide reading order, and create visual unity? For each job, identify specific elements that succeed or fail.

Guidance Choose a figure you can look at carefully. Annotate it. For each job, identify the specific visual choice that supports or fails it. For comparison: are scales shared? are panels aligned? For hierarchy: is there a clear hero? For reading order: does the sequence match a logical argument? For unity: is the typography consistent? Are the colors consistent? The exercise is training your eye, not finding perfect figures.

B.9 ★★★ | Create

Design a small-multiple layout showing daily COVID case counts for 20 countries over 30 days. The layout will be used as a static image on a news website. Specify: the grid arrangement (rows × columns), the aspect ratio of each panel and the whole figure, whether you use shared or free y-axes (and why), the order of the panels, the chart title, and the source attribution.

Guidance 4×5 or 5×4 grid. Each panel is a small time-series line chart. Panel aspect ratio: close to square (maybe 3:2). Overall figure: roughly square or slightly wide. Shared x-axis (30 days). Y-axis: probably shared (same scale) so magnitudes are comparable — unless the range is so different across countries that shared would hide the pattern in smaller countries. Order: by total case count, or by geography. Figure title: an action title describing the main finding. Source: Johns Hopkins or Our World in Data.

B.10 ★★★ | Create

Design a dashboard layout for monitoring a data pipeline. The dashboard needs to show: (1) current pipeline status (running / failed / success), (2) throughput over the last 24 hours as a line chart, (3) error rates by stage as a bar chart, (4) top 5 recent failures as a table, (5) a geographic map of source regions. Sketch the layout and justify each position choice using principles from this chapter.

Guidance Current status is probably the hero because it tells the viewer whether anything is broken right now — place it in the top-left, large, with a color (red/yellow/green) that is visible at a glance. Throughput line chart next to it (top right), because throughput over time is the second most-monitored thing. Error rates bar chart below the throughput (reading order: first you check status, then you check throughput, then you investigate errors). Top failures table below the status. Geographic map bottom row. Consistent typography across panels; accent color reserved for "problem" signals.

Part C: Synthesis and Design Judgment (5 problems)

C.1 ★★★ | Evaluate

The chapter argues that small multiples are "the best design principle for many visualization problems" (paraphrasing Tufte). Defend or critique this claim. Identify at least one class of problems where small multiples are clearly not the right choice.

Guidance Defense: small multiples solve the spaghetti-chart problem, enforce comparison, and scale gracefully to many groups. They are the right answer whenever you want to show the same kind of relationship across different slices of data. Critique: small multiples require that every panel have enough data to show a meaningful pattern, that the groups are comparable on a shared or carefully-justified free scale, and that the chart type works at small sizes. They fail with too-few data points per panel, with heterogeneous groups that do not belong on the same scale, or with chart types that do not shrink well.

C.2 ★★★ | Analyze

The chapter warns that small multiples with free (per-panel) y-axes can hide magnitude differences and potentially mislead. When is a free y-axis the honest choice, and when is it a shortcut that distorts the comparison?

Guidance Free y-axes are honest when the goal is to compare *shapes* or *patterns* across groups, not absolute magnitudes. For example, comparing the shape of adoption curves across 20 products where product sizes differ by 1000× — a shared y-axis would crush most curves into thin lines at the bottom, and the shape comparison would be lost. Free axes reveal the shape but require the reader to understand that they cannot compare absolute levels across panels. Shortcut/dishonest: using free axes because shared axes would "look bad" when the reader actually needs to see magnitude differences. The difference is in what comparison you are enabling and whether the reader understands the axis choice.

C.3 ★★★ | Create

Write a short "layout checklist" (6-10 items) that a colleague could apply to any multi-chart figure before publishing it. The checklist should capture the most important decisions from this chapter in a form that is short enough to scan and concrete enough to act on.

Guidance Candidate items: Are the panel edges aligned to a visible grid? Do the panels share axes where appropriate? Is the hero clearly larger or more prominent than the supporting panels? Does the panel order match the reading order (Z-pattern)? Is the typography consistent across all panels? Is the color palette consistent? Is there enough whitespace between panels? Do you have a figure-level title in addition to panel titles? Is there an on-figure source attribution? Would a first-time reader understand the figure in under 10 seconds?

C.4 ★★★ | Evaluate

The chapter treats composition as a design discipline separate from single-chart design. Is this separation useful, or does it create artificial boundaries? Argue for your position.

Guidance Separation is useful because composition requires decisions (alignment, hierarchy, reading order) that do not arise in single-chart design. But the separation can be misleading if practitioners think of composition as "what you do after the charts are done" — in practice, the composition decisions affect the design of individual charts (you might choose different chart types to fit a layout). The best answer probably acknowledges both sides: composition is a distinct discipline, but good designers think about composition and single-chart design together.

C.5 ★★★ | Create

Pick a dataset you have worked with recently. Design a small-multiple figure using that dataset. Be specific about: the grouping variable (what defines the panels), the shared chart type (what every panel shows), the shared and free axes, the panel order, the overall figure title, and at least one annotation you would add.

Guidance The point is to apply the principles to your own data. A common pattern: a small multiple of 6-12 panels, one per category in your data, each showing a time series or distribution. Annotate at least one panel with a callout about its most interesting feature. Make all the design decisions explicit, and be able to defend each one using principles from the chapter.

These exercises develop compositional judgment, which is harder to acquire than single-chart judgment because it requires holding multiple charts in mind simultaneously. Sketching on paper forces you to commit to layouts in a way that screen-based tools often let you avoid. Do at least three of the Part B exercises on paper before moving on to Chapter 9.