Professor Buckingham, a chemist and teacher at a community college, is organising his graduated cylinders in the hopes of keeping his office tidy and setting a good example for his students. He has beakers with diameters, in inches, of $\displaystyle\frac{1}{2}, \frac{3}{4}, \frac{4}{5}, 1$ and $\displaystyle\frac{5}{4}$. With his original five cylinders, professor Buckingham realises that he is missing a cylinder necessary for his upcoming lab demonstration for Thursday's class. He remembers that the cylinder he needs when added to the original five, will create a median diameter value of $\displaystyle\frac{9}{10}$ for the set of six total cylinders. He also knows that the measure of the sixth cylinder will exceed the value of the range of the current five cylinders by a width of anywhere from $\displaystyle\frac{1}{4}$ inches to $\displaystyle\frac{1}{2}$ inches, inclusive. Based on the data, what is one possible value of y, the diameter of this missing sixth cylinder?