GB-32-03-001 · Box-plot comparison
A set of test scores has lower quartile 11, median 21 and upper quartile 40.
(a) Calculate its interquartile range.
(b) Another set has median 26 and IQR 36. Compare the typical score and the spread.
Part (a)
Box Plots: Interquartile Range & Comparing
Booklet p. 70 & p. 71
Method
1) IQR = Upper Quartile (UQ) − Lower Quartile (LQ)
2) Compare medians (average) and IQRs (spread/consistency) in context
Worked Example (GB-32-03-001 · Part (a))
Calculate its interquartile range.
1)
29
Ans =
29
Part (b)
Box Plots: Interquartile Range & Comparing
Booklet p. 70 & p. 71
Method
1) IQR = Upper Quartile (UQ) − Lower Quartile (LQ)
2) Compare medians (average) and IQRs (spread/consistency) in context
Worked Example (GB-32-03-001 · Part (b))
Another set has median 26 and IQR 36. Compare the typical score and the spread.
Booklet p. 71 — Must write 2 sentences in context:
1) Compare Medians (On average): State which group has a higher/lower median and what that means in context.
2) Compare IQRs (Spread / Consistency): State which group has a smaller IQR and is therefore more consistent / less spread out.
• Higher typical score, supported by the medians.
• Greater middle-half spread, supported by the IQRs.
The second set has higher median and greater spread in its middle half.