plotting data between concentric circles of known radii

I have a vector of 1000 random numbers biased towards the bounds of 540 and 600. I need to plot this data as a wriggly circular path between two concentric circles of radii 540 and 600 respectively. How do I do this? Presently, I'm able to plot the concentric circles of given radii, but if I try to plot the given random data which is between the bounds 540 and 600, it is plotted along the width between the two concentric circles. I want it to be plotted as a noisy circular curve between the concentric circles. I hope I'm able to explain my point If anyone can tell me, how do I do that. Thanks