How to calculate a frequency curve from a sample of values, and interpolate between curves

Question

I have a set of about 500 values, from which I'm currently plotting a histogram.

I'd like to plot a frequency curve, i.e. go from the left two graphs to the rightmost on the below image borrowed from Wolfram MathWorld.

If I can manage this, I'll then have frequency curves for various points in time. I'd like to smoothly interpolate between them.

i.e. if I have a frequency curve at 1 month, another at 3 and another at 6, I'd like a function that accepts a range and a time, and returns the approximate frequency of that range at that point in time.

I don't really know where to begin with this. Any pointers on what I should read up on to accomplish this? And any ideas as to how can I go about doing it?

Edit

By "maintain the peak throughout" I mean that interpolating between two curves like these two:

Should not result halfway in a curve that looks like this:

But should look like this: