Data and Displays · Challenge problem

A histogram is drawn correctly with unequal bins, so each bar's height is a density (values per unit of width). The bars are: $0$–$10$ height $1.2$; $10$–$20$ height $2.0$; $20$–$40$ height $1.5$; $40$–$80$ height $0.25$. Assuming the values are spread evenly within each bin, estimate the median. Give an exact answer.