answer:Are the midpoints equally spaces out? You may have to assume they are unless you have more information. If so, say you have midpoints m1, m2, ..., mn The lower class limit for, say, m7 would be (m6 + m7)/2 The upper class limit for m7 would be (m7 + m8)/2 Also, this means that you know the width of each class (the different between the upper class limit and the lower class limit). Say thats w. So the lower class limit for m1 is m1 – w/2 And the upper class limit for mn is mn + w/2 These are special cases since there is no m0 or m(n+1).