You could consider the width of the 'slots' in the sprocket to be the hole 'diameter' d. (ref the edited pic, attached)
If you measure the center hole diameter (which you did) and the distance between the edge of the center hole and inner edge of a slot (S1), you could calculate the innermost possible mounting circle. And, if you measure from the edge of the center hole and the outer edge of the slot (S2), you could calculate the outermost possible mounting circle diameter.
It's my guess that the slot is configured so that the middle of the slot corresponds to the desired mounting hole circle, but, they knew that the tolerances they were getting were poor...