For grouped and censored data from an exponential distribution, the method of maximum likelihood (ML) does not in general yield a closed form estimate of the mean, and therefore, an iterative procedure must be used. This paper considers three approximate estimators of the mean: two approximate ML estimators and the mid-point estimator. Their performances are compared by Monte Carlo simulation to those of the ML estimator in terms of the mean square error and bias. The two approximate ML estimators are reasonable substitutes for the ML estimator unless the probability of censoring and the number of inspections are small. The effect of inspection schemes on the relative performances of the three approximate methods is investigated.