77. 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. Institut. Engrs., 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 Freq. 6 23 30 35 32 xn ns2n

1  1n  12s2n



n n  1 1xn1  xn 22 xn1 xn xn1 xn x

x x

Length 16—18 18—20 20—22 22—24 24—26 Freq. 48 42 40 28 27 Length 26—28 28—30 30—35 35—40 40—45 Freq. 26 14 27 11 2

a. Draw a histogram corresponding to these frequencies.

b. What proportion of these route lengths are less than 20? What proportion of these routes have lengths of at least 30?

c. Roughly what is the value of the 90th percentile of the route length distribution?

d. Roughly what is the median route length?