Where should the box and whiskers end?
You will be able to: Construct a modified boxplot and apply explicit outlier rules.
Where should the box and whiskers end?
Seven waits cluster between 2 and 10 minutes, while one is 30. A boxplot summarizes the middle while marking that long wait separately.
A useful starting point: What happens when the measurement scale changes? →
Words and symbols before equations
- Five-number summary
- Minimum, Q₁, median, Q₃ and maximum.
- Fence
- A calculated threshold used to flag possible outliers.
- Modified boxplot
- Whiskers end at the most extreme non-outliers; outliers are plotted separately.
- Potential outlier
- A flagged observation to investigate, not automatically an error.
What this picture assumes
Data: 2,4,4,6,8,10,10 and the adjustable maximum. Quartiles use medians of the halves. Modified boxplot flags strictly beyond 1.5-IQR fences. The two-s screen uses sample s here and may differ.
Read the picture in three steps
- Read the axes and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- n=8; mean 9.25, median 7, sample s 8.876, IQR 6, range 28 minutes. Fences -5, 19; IQR outliers: 30. Two-s screen: 30. 87.5% at or below 10 minutes.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the mathematics
Using 2,4,4,6,8,10,10,30, the quartiles are 4 and 10, so IQR=6. The 1.5-IQR fences are 4−9=−5 and 10+9=19 minutes.
The value 30 exceeds 19. Draw the box from 4 to 10, a median line at 7, whiskers to 2 and 10, and a separate mark at 30. Whiskers do not end at the fences.
Another screening rule flags values more than two standard deviations from the mean. Different rules can flag different points; specify which one you use. Neither rule authorizes deleting real data. A boxplot also hides clusters and exact values, so inspect the raw-data plot.
A worked example, step by step
Construct a modified boxplot for 1,2,3,4,5,6,7,20 using median-of-halves quartiles.
- Median is 4.5; Q₁=(2+3)/2=2.5; Q₃=(6+7)/2=6.5.
- IQR=4, giving fences −3.5 and 12.5.
- Only 20 is beyond a fence; whiskers reach 1 and 7.
- Draw the box from 2.5 to 6.5, median 4.5, and a separate point at 20. The five-number summary still includes the actual maximum 20.
Fences are decision thresholds, not observed values or automatic whisker endpoints.
Is a value exactly on a 1.5-IQR fence flagged by this rule?
Compare with an explanation
No; the rule uses strictly beyond the fence.
Predict. Change one thing. Explain.
Move the largest wait. Identify when it becomes an IQR outlier and compare with the two-standard-deviation screen. Watch the whisker move to an observed non-outlier.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
n=8; mean 9.25, median 7, sample s 8.876, IQR 6, range 28 minutes. Fences -5, 19; IQR outliers: 30. Two-s screen: 30. 87.5% at or below 10 minutes.
| Summary | Value |
|---|---|
| Data | 2, 4, 4, 6, 8, 10, 10, 30 |
| Mean | 9.25 |
| Median | 7 |
| Sample variance | 78.786 squared units |
| Sample s | 8.876 |
| Q₁ / Q₃ | 4 / 10 |
Data: 2,4,4,6,8,10,10 and the adjustable maximum. Quartiles use medians of the halves. Modified boxplot flags strictly beyond 1.5-IQR fences. The two-s screen uses sample s here and may differ.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using the data values, graph scales, summary statistics or study-design conditions. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionQ₁=10, median=14, Q₃=18, minimum=6, maximum=40; largest non-outlier is 25. Find fences and describe the modified boxplot.
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Compare with the answer and four-point rubric
- 1 point: IQR=8.
- 1 point: Fences are −2 and 30.
- 1 point: 40 is flagged; 6 and 25 are within the fences.
- 1 point: Box 10 to 18, median 14, whiskers 6 and 25, separate mark 40.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What are the five summary values?
Minimum, Q₁, median, Q₃, maximum.
RECALL 2Should an outlier automatically be removed?
No; investigate the measurement and context.
RECALL 3Can a boxplot reveal two clusters reliably?
No; use a display of more detailed distribution shape.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Where should the box and whiskers end?
- Fences: Q₁−1.5 IQR and Q₃+1.5 IQR.
- Flag values strictly beyond a fence.
- The box spans the middle half; its length is IQR.
Remember: Fences are decision thresholds, not observed values or automatic whisker endpoints.
Conditions: Data: 2,4,4,6,8,10,10 and the adjustable maximum. Quartiles use medians of the halves. Modified boxplot flags strictly beyond 1.5-IQR fences. The two-s screen uses sample s here and may differ.
Refresh Kid · AP Statistics Unit 1 · Objectives 1.7.D, 1.8.A, 1.8.B · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 1.8, objectives 1.7.D, 1.8.A, 1.8.B. Framework effective Fall 2026, checked September 17, 2026. Unit 1 includes one-variable data and data collection; it is part of the revised five-unit course.
Examples and datasets are synthetic, independently authored teaching material. Quartile calculations state a median-of-halves convention. Outlier screens identify values to investigate, not data to discard. Random selection and random assignment have different inferential roles. These lessons introduce design and descriptive reasoning; formal inference comes in later units.
The Organic Chemistry Tutor companion title and destination were checked; the full video was not reviewed. Khan Academy’s destination was checked, but its lesson content was not fully readable by the research tool. OpenStax provides optional reference reading. No provider scripts, questions or graphics were copied. Refresh Kid is not affiliated with these providers.
GitHub’s 3D website collection informed optional spatial inspection. Our original sampling model uses self-hosted Three.js with its MIT license. It shows labeled units in four groups; camera rotation does not change the sampling procedure. Quantitative graphs remain 2D to avoid perspective distortion. Complete labeled diagrams, selected IDs and explanations remain available without 3D.
Independent teacher review and observation of students remain pending. Technical checks do not certify statistical accuracy, accessibility or learning effectiveness. This is a review edition.
Released AP Statistics questions and scoring guides are optional. Older exams use the earlier framework, so check alignment before selecting parts. All practice on this page is original, not official AP material.
Learn → Explore → Practice → Review is informed by the IES learning guide. This implementation has not yet been evaluated with learners.
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