A city transport department recorded the daily number of passengers (in thousands) carried by one of its bus routes for 60 consecutive days. The observations were grouped into six equal classes 10–15, 15–20, 20–25, 25–30, 30–35 and 35–40 and plotted as a histogram whose bar heights (in cm) are listed below in order:
2.0, 4.5, 10.0, 8.5, 3.5, 1.5
The drawn scale is 1 cm = 2 days on the frequency axis.
(a) Form the frequency distribution table corresponding to the histogram.
(b) Calculate the cumulative frequencies and draw a ‘less-than’ cumulative frequency table.
(c) Using the cumulative frequencies, determine the median class and estimate the median number of passengers carried per day (take the class size h=5).
(d) Estimate the number of days on which the passenger count exceeded 28 000 and express this as a percentage of the total number of days.
(e) Comment on any two features of the passenger demand pattern that a transport planner should consider, based on the shape of the histogram.