What you’ll learn
Interpret variability.
Key idea
Keep measurement units; a quartile width is not a count of students or a required pairwise gap.
IQR is a sample's central interval width with measurement units; box position is not width, and no single IQR fixes every pairwise gap.
Worked example
Classify examples and non-examples for the concept 'Interpret variability'.
For sample (2, 10, 18, 26, 34, 42, 50, 58) minutes, median-of-halves gives Q1=14,Q3=46. Classify 'every pair of observed times differs by exactly 32 minutes'.
- The sample quartile interval spans Q1=14 to Q3=46, width 32 minutes.
- This describes the central-half span, not every pairwise difference; a second box from 22 to 38 has smaller width 16.
Answer: Non-example — IQR 32 is the quartile interval's width, not every pair's separation.
Quick Check
Classify examples and non-examples for the concept 'Interpret variability'.
For sample (6, 7, 8, 9, 10, 11, 12, 13) minutes, median-of-halves gives Q1=15/2,Q3=23/2. Classify 'the quartile interval has width 4 minutes'.