Range, fences and boxplots
A boxplot gives a compact picture of the middle, spread and unusual values. A review flag is a reason to check a record, not a command to delete it.
Range = maximum minus minimum; distinguish this width from the endpoint interval. It depends only on two values. When you add observations without removing any, the range cannot shrink, although it can stay unchanged. SD and IQR can rise or fall as new data arrive; they do not have the same monotonic property.
Lower fence = Q1 - 1.5 times IQR. Upper fence = Q3 + 1.5 times IQR. A typical Tukey boxplot has a box from Q1 to Q3, a median line, and whiskers at the most extreme observed values still inside the fences. The whiskers are not the numerical fence locations. Points beyond the whiskers are candidates for review.
Using lecture quartiles 58.3 and 73.6, IQR = 15.3, and fences are 35.35 and 96.55 points. A score of 99 is flagged but still lies within a documented 0-100 scale. Verify the record before deciding what to do.
In the eight-number practice list, multiplying 75 by 10 changes the mean from 55 to 139.375 and the range from 40 to 715; sample SD becomes about 247.031. Median remains 55 and median-of-halves IQR remains 25 because the middle positions used have not changed. This illustrates robustness in this example, not immunity to every possible contamination pattern.
Sources: W2 PDF pp. 2-60; L2 Sections 1-8. The personalised Lab 2 has 240 synthetic students, unlike the 1,200-student lecture dataset. Do not mix their numbers.
The lecture's robust summaries are tested by changing one extreme value. The lab also makes the quartile convention explicit.
The lecture's fences and whiskers become record-level checks. Programme summaries and two equal-mean/SD classes show why the whole shape matters.
An IQR flag describes unusualness, while the dictionary and source establish different evidence. Deleting verified older students changes the population behind a rate.
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.
Q1=20 and Q3=24. What is the upper review fence?
The upper fence is 30 and the largest observation within it is 28. Where is the Tukey whisker?
2. Application
Apply the concept to a case or calculation.
Q1=10, Q3=18. What is the lower fence?
Does a value inside the fences have to be accurately recorded?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
For [3,5,9], adding 7 changes the range how?
A verified score 99 exceeds the upper fence on a 0–100 exam. What is supported?
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
It cannot shrink. It increases if a new value goes beyond an old endpoint; otherwise it stays the same. SD and IQR do not share this rule.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
No. Check source accuracy, measurement rules and the target population. Deleting a valid unusual person can distort who is represented.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?