Where and why do we plot points on cumulative frequency graphs?

At the end of each group. Say you have a table of groups and frequencies corresponding to those groups, for example for x we have group 0<x<=5 with frequency 6 and group 5<x<=15 with frequency 10. The cumulative frequency graph represents the total frequency below a certain value for x. Looking at the first group, all the 6 values for x could be 1. They could also be 2 ,3, 4 or 5 or even fractions. Or they could be mixed. The information given to us means that by the end of the group (when x=5), there are a total of 6 numbers. Therefore we plot the cumulative frequency at the highest value of the group. The point here is that cumulative graphs are an estimate because they are drawn with little information.