Calculate height of histogram bins from empirical distribution function I have an empirical distribution function:

And I need to calculate the height of each of the bins[0,1], (1,3], (3,5], (5,8], (8,11], (11,14], and (14,18]. The formula to get the height is: 
(# of elements in the bin)/(# of total elements)*(width of the bin). My issue here is, how can I tell how many elements are in the bin, and how many elements there are total given only the empirical distribution function? 
 A: You can make a 'density' histogram, but not one showing actual frequencies.
You have 8 interval boundaries (cutpoints) and hence 7 histogram bars.
From your cumulative relative frequencies, you can get the relative
frequencies of of the 7 intervals (bins):  0.125, 0.120, 0.170, 0.220, 0.070, 0.105, 0.190.
The relative frequency of a bin is (# in bin)/(total # in sample).
As you have noted, you do not know either the numerator or the denominator. However, you
do know the 7 ratios by subtraction as in the last paragraph.
Ordinarily, it is not good practice to use unequal bin widths unless
there is a very good reason (such as an extremely skewed distribution).
But this is an exercise on how to deal with unequal bin widths.
Just find the 7 bin widths and you can finish the problem.
Addendum: When you're done, the total area of all the bars in the histogram must be 1:
$$ \sum A_i = \sum w_ih_i   = \sum w_i(r_i/w_i) = \sum r_i = 1,$$
were sums are taken over all bins, $A_i$ is bar area, $w_i$ is bin width,
$h_i$ is bar height, and $r_i$ is the relative frequency of the bin.
The vertical axis of such a 'density' histogram (with unequal bin widths)
must be labeled 'Density' (not 'relative frequency').
