It is a robust and highly efficient estimator of the population spatial-median (also called the "L1 median").
Despite its simplicity, the trimean is a remarkably efficient estimator of population mean.
Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance.
Thus an efficient estimator need not exist, but if it does, it is the MVUE.
In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some "best possible" manner.
Finite-sample efficient estimators are extremely rare.
Thus, the sample mean is a finite-sample efficient estimator for the mean of the normal distribution.
For some estimators, they can attain efficiency asymptotically and are thus called asymptotically efficient estimators.
Despite its simplicity, for estimating the standard deviation of a normal distribution, the scaled interdecile range gives a reasonably efficient estimator.
Estimators with low efficiency require more independent observations to attain the same sample variance of efficient unbiased estimators.