We report the rest-frame ~ 0.1 - 5 year X-ray variability properties of an unbiased and uniformly selected sample of 24 broad absorption line (BAL) and 35 mini-BAL quasars from the SDSS DR16Q catalog, making it the largest representative sample used to investigate such variability. Eight BAL and twelve mini-BAL quasars exhibit significant variability beyond that expected from the measurement errors, which is more than twice the number found in previous sample studies. The distributions of X-ray variability amplitudes in both populations are consistent with a Gaussian distribution. We also compare these distributions with the variability amplitude distribution of matched sample of 91 radio-quiet, non-BAL quasars. We find that the variability amplitude distributions of all three populations are statistically similar.