For context, the best single point estimate by L-estimators is the median, with an efficiency of 64% or better (for all n), while using two points (for a large data set of over 100 points from a symmetric population), the most efficient estimate is the 29% midsummary (mean of 29th and 71st percentiles), which has an efficiency of about 81%. Using quartiles, these optimal estimators can be approximated by the midhinge and the trimean.
In context, the median provides the best single point estimate with an efficiency of 64% or better (for all n), whereas using two points for a large data set over 100 from a symmetric population, the most efficient estimate is the midsummary (mean of the 29th and 71st percentiles), which has an efficiency around 81%. Using quartiles, these optimal estimators can be approximated by the midhinge and the trimean.