Continuous quantum variables can be made discrete by binning together their different values, resulting in observables with a finite number "d" of outcomes. While direct measurement indeed confirms their manifestly discrete character, here we employ a salient feature of mutual unbiasedness to show that such coarse-grained observables are of a different kind, being in a sense neither continuous nor discrete. In particular, we study periodic binning of continuous observables and prove that the maximum number of mutually unbiased measurements of this type equals three for even d, which is analogous to the continuous case. On the other hand, for odd d we can find more mutually unbiased measurements, though the known results for discrete systems are not entirely reproduced. However, we can show that there are never more than d + 1 in general, which is a known feature of discrete systems. To illustrate and explore these results, we present an example for construction of such measurements and employ it in an optical experiment confirming the existence of four mutually unbiased measurements with d = 3 outcomes in a continuous variable system.