  Mean profiles are widely used as indicators of the electricity consumption
habits of customers. Currently, in \'Electricit\'e De France (EDF), class load
profiles are estimated using point-wise mean function. Unfortunately, it is
well known that the mean is highly sensitive to the presence of outliers, such
as one or more consumers with unusually high-levels of consumption. In this
paper, we propose an alternative to the mean profile: the $L_1$-median profile
which is more robust. When dealing with large datasets of functional data (load
curves for example), survey sampling approaches are useful for estimating the
median profile avoiding storing the whole data. We propose here estimators of
the median trajectory using several sampling strategies and estimators. A
comparison between them is illustrated by means of a test population. We
develop a stratification based on the linearized variable which substantially
improves the accuracy of the estimator compared to simple random sampling
without replacement. We suggest also an improved estimator that takes into
account auxiliary information. Some potential areas for future research are
also highlighted.
