Visualizing Proportions

Parts of a Whole

STAT 80: Data Visualization

Week 5, Day 1

Visualizing Proportions

Today’s focus:

• What are proportions and why visualize them?
• Pie charts (yes, really!)
• Side-by-side bars
• Stacked bars
• The great pie chart debate

What Are Proportions?

Proportion = parts of a whole

Everyday examples:

• Budget breakdown (rent, food, entertainment)
• Market share (which companies dominate)
• Demographics (age groups, ethnicities)
• Time allocation (work, sleep, leisure)

Key features:

• Values add up to 100% (or 1.0)
• Show how a total is divided
• Answer “how much of the whole?”

Not proportions:

• Quantities that don’t sum to a total
• Separate measurements that happen to be percentages

Why Proportions Matter

Understanding proportions helps us answer:

• Composition: What makes up this total?
• Comparison: Which part is biggest?
• Change: How has the makeup shifted over time?
• Balance: Is it evenly distributed or dominated by one part?

Good proportion visualizations make these answers obvious at a glance

The Infamous Pie Chart

Most loved and most hated chart in data visualization!

Let’s understand why…

Pie Chart: How It Works

Each slice:

• Represents one category
• Size (angle) = proportion of total
• All slices = 360° = 100%

Reading it:

• Compare slice sizes
• Look at slice labels
• Assess overall breakdown

When Pie Charts Work Well

Pie charts are good when:

1. ✅ You have few categories (3-5 ideal, 7 max)
2. ✅ One part is clearly dominant (>50%)
3. ✅ You want to emphasize parts of a whole
4. ✅ Rough comparisons are enough (not precise differences)

Example: Market share

Good Pie Chart Example

Why it works:

• Only 4 categories
• Housing clearly dominates
• Purpose is showing budget composition
• Easy to see approximate proportions

When Pie Charts Fail

Pie charts are bad when:

1. ❌ Too many categories (more than 7)
2. ❌ Slices are similar sizes (hard to compare angles)
3. ❌ Precision matters (exact percentages needed)
4. ❌ Comparing multiple pies side-by-side
5. ❌ Small differences are important

Bad Pie Chart Example 1

Too many slices!

• Hard to distinguish similar colors
• Tiny slices are unreadable
• Legend is too long
• Can’t compare angles accurately

Bad Pie Chart Example 2

Slices too similar!

Which is bigger: Blue or Green? Red or Orange?

Angles are hard to compare precisely

Our eyes are bad at judging angles!

Bad Pie Chart Example 3

Comparing multiple pies is terrible!

• Can’t line up slices to compare
• Different sizes make comparison worse
• What changed between Year 1 and Year 2?

The Great Pie Chart Debate

Team Anti-Pie 🥧❌

• Humans bad at judging angles
• Bars are always clearer
• “Friends don’t let friends use pie charts”
• Research shows alternatives are better

Team Pro-Pie 🥧✅

• Everyone understands them
• Good for parts-of-whole
• Sometimes the right tool
• “It depends on the situation”

Marcela’s take: Pie charts have their place, but that place is narrow. When in doubt, try alternatives first! and NEVER, NEVER, NEVER use 3D pies.

Alternative 1: Simple Bar Chart

Instead of pie, use bars!

Advantages:

• ✅ Easy to compare lengths
• ✅ Can order by size
• ✅ More precise comparisons

Alternative 2: Stacked Bar Chart

Shows proportions and maintains “parts of a whole” feeling

• Total bar = 100%
• Segments = categories
• Keeps compositional context

Stacked Bars vs Pie

Stacked Bar ✅

• Easy to compare to edges
• Can stack multiple bars for comparison
• Linear comparisons

Pie ⚠️

• Harder to compare angles
• Multiple pies get messy
• Circular comparisons

Side-by-Side Bars for Comparison

When comparing proportions across groups:

Each group gets its own set of bars

Easy to compare categories across groups!

Stacked vs Side-by-Side Bars

Stacked bars:

• Show overall composition
• Emphasize totals
• Compare first category easily (aligned to baseline)
• Hard to compare middle categories

Side-by-side bars:

• Compare categories across groups
• See each value clearly
• Don’t show total as obviously
• Take more space

Stacked Bar Challenge

Question: Which is larger in Group 2: Category B or Category C?

Hard to tell! They don’t share a baseline

This is the main weakness of stacked bars

Design Choices for Proportion Charts

Ordering:

• For pies: Start at 12 o’clock, go clockwise from largest to smallest
• For bars: Order by size (unless natural order exists)

Colors:

• Limit palette to 5-7 distinct colors
• Use color to highlight important categories
• Keep it accessible (colorblind-friendly)

Labels:

• Include percentages when precision matters
• Put labels inside slices/bars when they fit
• Use leader lines sparingly

Pie Chart Design Best Practices

If you must use a pie chart:

1. Explode important slices slightly (pull out from center)
2. Order slices from largest to smallest
3. Start at 12 o’clock position
4. Limit to 5-7 categories maximum
5. Label directly on slices when possible
6. Avoid 3D effects (they distort proportions!)

The Dreaded 3D Pie

Never. Use. 3D. Pies. 🚫

• Perspective distorts proportions
• Slices in “front” look bigger
• Adds no information, reduces accuracy
• Peak “chartjunk”

Donut Charts

Pie chart variation: hollow center

Same strengths and weaknesses as pie charts, but:

• ✅ Can put text/numbers in the center
• ✅ Slightly less emphasis on “whole”
• ❌ Even harder to compare angles

When Should You Show Proportions?

Good reasons:

• Data naturally represents parts of a whole
• You want to show composition
• Percentages are meaningful

Watch out for:

• Forcing percentages when counts matter more
• Using proportions to hide small sample sizes
• Comparing proportions across very different totals

Example: “90% approval!” sounds great, but what if only 10 people were surveyed?

Showing Sample Size

When showing proportions, consider showing the denominator:

Include sample size:

• In title: “Customer Satisfaction (n=347)”
• In caption: “Based on 1,250 responses”
• In the visualization itself

Special Case: 100% Stacked Bars

Comparing proportions across many groups:

All bars reach 100%, easy to compare composition

Good for: Seeing how proportions change across groups

Bad for: Comparing actual quantities (bars are same height!)

Summary: Choosing Your Chart

Chart Type	Best For	Avoid When
Pie	3-5 categories, one dominant	Many categories, precise comparison
Donut	Same as pie + center annotation	Multiple donuts side-by-side
Simple bar	Precise comparison, ranking	Need to emphasize “whole”
Stacked bar	Composition over time/groups	Comparing middle segments
Side-by-side	Comparing across groups	Space is limited

Activity: Critique These Charts

For each chart:

1. What works well?
2. What doesn’t work?
3. How would you improve it?
4. What alternative would you suggest?

Next Class Preview

Thursday: We level up to nested proportions!

• Mosaic plots
• Treemaps
• Nested pies (pies within pies!)
• Parallel sets
• Showing hierarchies and sub-categories

Plus: Tableau guidance on all these techniques!

Remember

“The only thing worse than a pie chart is several of them.”

— Edward Tufte (data visualization expert)

But also remember:

Sometimes a simple pie chart is exactly what your audience needs. Know the rules, then know when to break them thoughtfully!