Box plots, fences and whiskers
A box plot shows the median, the middle half of the data and unusual values. Fences decide what is flagged; whiskers stop at real observations.
A box plot summarises location and spread (W6 pp. 14-15). For 2, 4, 4, 4, 6, 8, 10, 10, 12, 30 (n=10):
- Median = (6+8)/2 = 7, the middle line.
- Q1 = 4 and Q3 = 10 (medians of the lower and upper five values), forming the box. IQR = 10-4 = 6.
- Lower fence = Q1-1.5×IQR = 4-9 = -5; upper fence = Q3+1.5×IQR = 10+9 = 19.
- Whiskers reach the most extreme observed values inside the fences: 2 and 12.
- 30 lies beyond the upper fence and is drawn as a separate flagged point.
Fences are calculated cut-offs; whiskers are drawn to real observations, so they usually stop short of the fences. A flag does not prove a data error: 30 could be a genuine heavy user. Check the source before excluding anything (Week 3, lesson 4.10). Different software quartile conventions can shift Q1 and Q3 slightly; state the convention.
A box plot hides sample size and shape: two very different distributions, including a bimodal one, can share the same box. Put n beside each box and pair box plots with a histogram or jittered points when shape matters.
Source: W6 PDF pp. 1-37. Most numbers in the lecture are illustrative or constructed for teaching; pp. 26-27 reuse the Week 5 synthetic registration counts. The Week 6 lab manual (L6) practises Week 5 EDA reasoning and is worked through section by section in Lab work.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
For Q1=4 and Q3=10, what is the upper fence?
For 2, 4, 4, 4, 6, 8, 10, 10, 12, 30 with fences −5 and 19, where do the whiskers end?
2. Application
Apply the concept to a case or calculation.
What is the median of 2, 4, 4, 4, 6, 8, 10, 10, 12, 30?
Q1=4 and IQR=6. What is the lower fence?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
A value lies beyond the upper fence. What does that show?
What can a box plot hide?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
−5 and 19 are the fences, which are calculated limits. Whiskers stop at the most extreme observed values inside those limits, which are 2 and 12.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Check its source and context. It could be a genuine heavy user, so keep it unless evidence shows it is invalid, and report how the conclusions change if it is excluded.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?