Atomic clocks are essential elements in a variety of applications, such as global navigation satellite systems. Consequently, monitoring their performances is fundamental. The Allan variance is the key statistical tool for the performance characterization of atomic clocks. This paper proves that the Allan variance computed from frequency measurements with missing data is affected by a bias, which can make it dramatically different from the expected behavior in the full data case. Furthermore, it shows how to eliminate (or largely reduce) this bias by correcting the Allan variance. The corrected Allan variance is obtained for some of the most common atomic clock noise components, and it is validated through numerical simulations.