Forty volunteers recorded their journeys on Route A, all leaving at 10:00 on weekdays. The grouped t

Question

Forty volunteers recorded their journeys on Route A, all leaving at 10:00 on weekdays. The grouped times are shown. The cumulative-frequency diagram represents the same grouped sample using straight segments. Route B has a separately collected sample with mean 26.0 min and standard deviation 8.0 min. Time t (min)Frequency $0<t\leq10$4 $10<t\leq20$10 $20<t\leq30$14 $30<t\leq40$8 $40<t\leq50$4 A traveller wants short journey times that are also consistent. Compare Routes A and B, supporting your advice with suitable estimated numerical measures of journey time and spread. Show how you obtain your measures from the grouped data.[7] Use the cumulative-frequency graph to estimate the lower and upper quartiles and hence the interquartile range for Route A.[2] Give one reason why these data may not represent all journeys made on Route A, and identify a group of journeys that may be under-represented.[1]

Accepted Answer

(a) A estimated mean 24.5 min, SD 11.2 min: A shorter on average; B more consistent. No dominance. (b) Q 1≈16 min,Q 3≈32.5 min,IQR≈16.5 min. (c) Only weekday 10:00 departures sampled.

Time t (min)	Frequency
\(0<t\leq10\)	4
\(10<t\leq20\)	10
\(20<t\leq30\)	14
\(30<t\leq40\)	8
\(40<t\leq50\)	4

Comparing journey-time distributions

Comparing journey-time distributions

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