Textbook Problem

Lengths of bus routes for any particular transit system will typically vary from one route to another. The article “Planning of City Bus Routes” (J. of the Institution of Engineers, 1995:211-215) gives the following information on lengths (km) for one particular system:

Length	6−<8	8−<10	10−<12	12−<14	14−<16
Frequency	6	23	30	35	32
Length	16−<18	18−<20	20−<22	22−<24	24−<26
Frequency	48	42	40	28	27
Length	26−<28	28−<30	30−<35	35−<40	40−<45
Frequency	26	14	27	11	2

1. a. Draw a histogram corresponding to these frequencies.
2. b. What proportion of these route lengths are less than 20? What proportion of these routes have lengths of at least 30?
3. c. Roughly what is the value of the 90^th percentile of the route length distribution?
4. d. Roughly what is the median route length?