80. 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 Frequency 6 23 30 35 32 Length Frequency 48 42 40 28 27 Length Frequency 26 14 27 11 2 262,28 282,30 302,35 352,40 402,45 162,18 182,20 202,22 222,24 242,26 62,8 82,10 102,12 122,14 142,16 sn 2 xn xs n11 n11 2

nsn11 2 5 (n 2 1)sn 2 1 n

n 1 1

(xn11 2 xn)2 xx n11 n xn11 xn11 sn11 x 2 x1 n11 ,

c, xn sn 2 xn i 5 1, cz , n i 5 (xi 2 x)/s i 5 1, cy , n i 5 xi 2 x x

x1, x2,

c, xn

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?