How to Create a Boxplot for AP Statistics Questions | Step-by-Step Guide

Introduction: Why Boxplots Matter in AP Statistics

Boxplots (also called box-and-whisker plots) are a staple of AP Statistics. They appear in both Multiple Choice Questions (MCQs) and Free Response Questions (FRQs), especially in topics like data analysis, variability, and comparing distributions.

By mastering boxplots, you’ll be able to:

• Summarize large data sets visually.
• Identify outliers quickly.
• Compare multiple groups in one graph.
• Explain variability and spread using statistical vocabulary.

This guide — combined with RevisionDojo’s boxplot worksheets, practice problems, and step-by-step video tutorials — will teach you how to create, read, and analyze boxplots with confidence.

Step 1: The Five-Number Summary

To draw a boxplot, you need the five-number summary:

• Minimum (lowest data point).
• Q1 (first quartile, 25th percentile).
• Median (middle value, 50th percentile).
• Q3 (third quartile, 75th percentile).
• Maximum (highest data point).

👉 Example Data Set:
5, 7, 8, 10, 12, 15, 16, 18, 21, 25

• Min = 5
• Q1 = 8
• Median = 13.5
• Q3 = 18
• Max = 25

👉 RevisionDojo practice sets provide step-by-step breakdowns of five-number summaries.

Step 2: Drawing the Boxplot

Once you have the five-number summary:

1. Draw a number line covering your data range.
2. Mark the five-number summary.
3. Draw a box from Q1 to Q3.
4. Draw a line at the median.
5. Draw whiskers from Q1 → Min and Q3 → Max.

👉 The box shows the Interquartile Range (IQR), while whiskers show variability outside the middle 50%.

Step 3: Identifying Outliers

The AP Exam often tests your ability to find outliers. Use the 1.5*IQR Rule:

• IQR = Q3 – Q1
• Lower fence = Q1 – (1.5 × IQR)
• Upper fence = Q3 + (1.5 × IQR)

Any data point beyond these fences = outlier.

👉 Example:
Q1 = 8, Q3 = 18 → IQR = 10

• Lower fence = 8 – 15 = -7
• Upper fence = 18 + 15 = 33
  No data beyond this → no outliers.

👉 RevisionDojo worksheets include outlier detection drills.

Step 4: Types of Boxplots

• Regular boxplot: no outliers.
• Modified boxplot: outliers marked separately (dots or stars).
• Comparative boxplot: two or more groups side-by-side for comparison.

👉 FRQs often ask you to compare two boxplots — focusing on center, spread, shape, and outliers.

Step 5: Interpreting Boxplots

When interpreting, always comment on:

• Center: Median.
• Spread: Range or IQR.
• Shape: Symmetric vs skewed.
• Outliers: Mention if present.

👉 Example Interpretation:
“The distribution of test scores is slightly skewed right, with a median of 13.5, an IQR of 10, and no outliers.”

👉 RevisionDojo provides FRQ scoring guides for interpretation practice.

Step 6: Boxplots on the Calculator (TI-84 & Desmos)

• TI-84:
  • Enter data into STAT → EDIT.
  • 2nd → Y= → Plot 1.
  • Choose boxplot type.
  • Press ZOOM 9.
• Desmos:
  • Enter data list.
  • Use “boxplot” function.

👉 RevisionDojo offers calculator walkthroughs with screenshots.

Step 7: Common AP Exam Mistakes with Boxplots

• ❌ Forgetting to calculate quartiles correctly.
• ❌ Misidentifying outliers.
• ❌ Ignoring interpretation — just drawing the plot.
• ❌ Comparing distributions without mentioning context (e.g., “group A test scores higher than group B”).

👉 RevisionDojo practice FRQs train you to avoid these traps.

Step 8: Example AP Exam Problem

Question: The boxplots below compare math scores of two classes. Write a comparison.

Answer (Strong):
“Class A’s scores are higher on average (median 80 vs 72). However, Class B has greater variability (IQR 15 vs 10). Both distributions are roughly symmetric, and neither has outliers.”

👉 RevisionDojo provides sample high-scoring responses to model your answers.

Step 9: Why Boxplots Are Useful

• Handle large data sets without listing every point.
• Easily show variability and outliers.
• Great for comparing two or more groups.

This is why College Board loves them — they test interpretation, not just drawing.

Step 10: The RevisionDojo Advantage

RevisionDojo helps students master boxplots with:

• Step-by-step worksheets on five-number summaries.
• Outlier identification drills.
• Comparative boxplot FRQs.
• Calculator + Desmos tutorials.

👉 Check out RevisionDojo’s Boxplot Practice Resources here.

Frequently Asked Questions (FAQs)

Q: Do I need to draw boxplots by hand on the AP Exam?
A: Yes — for FRQs. MCQs may ask you to interpret them.

Q: Do I need exact fences for outliers?
A: Yes — use the 1.5*IQR rule. AP graders expect it.

Q: Is the mean shown on a boxplot?
A: No — only median is required.

Q: Do colleges use boxplots too?
A: Yes, especially in psychology, sociology, and business stats.

Q: How does RevisionDojo help with boxplots?
A: With worksheets, calculator tutorials, and comparative FRQ practice.

Final Thoughts

Boxplots are a foundational skill for AP Statistics. If you can confidently calculate the five-number summary, identify outliers, and compare groups, you’ll earn easy points on both MCQs and FRQs.

To succeed:

• Practice five-number summaries.
• Master the 1.5*IQR outlier rule.
• Always include context when interpreting.
• Use RevisionDojo’s resources to drill boxplot skills until automatic.

With this approach, you’ll turn every boxplot question into guaranteed points on the 2025 AP Statistics exam.