Question 1

Paper 2, calculatorMedium6 marks

A transport planner records journey times, tt minutes, for shuttle route Cedar. The cumulative frequency is the number of journeys with a time less than the upper boundary of the class.

Class intervalCumulative frequency at upper boundary
0≤t<50\leq t<51
5≤t<105\leq t<104
10≤t<1510\leq t<159
15≤t<2015\leq t<2019
20≤t<2520\leq t<2531
25≤t<3025\leq t<3038
30≤t<3530\leq t<3540

For estimates between class boundaries, assume the cumulative frequency graph consists of straight line segments and starts at (0,0)(0,0)

(a)

State the total number of journeys recorded for route Cedar.

[1]
(b)

Using a cumulative frequency graph, estimate the median and interquartile range of the journey times for route Cedar. Give your answers to the nearest 0.10.1 minute.

[3]
(c)

For route Birch, the lower quartile is 1212 minutes, the median is 1818 minutes and the upper quartile is 2424 minutes.

Hence compare the typical journey time and the spread of journey times for the two routes, using the medians and interquartile ranges.

[2]

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