The cumulative frequency graph represents 56 journeys on route A. For precise readings, its quartile points are (12, 14), (22, 28) and (30, 42). The horizontal axis is duration in minutes. Route B has median 21 minutes and interquartile range 16 minutes.
(a) Find the median and interquartile range for route A.
(b) Compare typical journey time and consistency for the two routes.
Part (a)Cumulative Frequency: Quartiles, IQR & Comparing DistributionsBooklet p. 69 & p. 71
Method
1) Read Median (Q₂) and calculate IQR = Q₃ − Q₁
2) Write 1 sentence comparing medians (average) and 1 sentence comparing IQRs (consistency) in context
Worked Example (RV-19-001 · Part (a))
Find the median and interquartile range for route A.
1)
Median = 22.
2)
IQR = 30 − 12.
3)
18 minutes.
Ans =Median 22 minutes; IQR 18 minutes.
Part (b)Cumulative Frequency: Quartiles, IQR & Comparing DistributionsBooklet p. 69 & p. 71
Method
1) Read Median (Q₂) and calculate IQR = Q₃ − Q₁
2) Write 1 sentence comparing medians (average) and 1 sentence comparing IQRs (consistency) in context
Worked Example (RV-19-001 · Part (b))
Compare typical journey time and consistency for the two routes.
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.
• Compare the medians in context.
• Compare the IQRs; the smaller IQR indicates more consistent times.
Route B has the shorter median time. Route B has the smaller IQR and is more consistent.