Experience with a variety of diffraction data-reduction problems has led to several strategies for dealing with mismeasured outliers in multiply measured data sets. Key features of the schemes employed currently include outlier identification based on the values ymedian = median(|Fi|2), σmedian = median[σ(|Fi|2)], and |Δ|median = median(|Δi|) = median[||Fi|2-median (|Fi|2)|] in samples with i = 1, 2 ..... n and n ≥ 2 measurements; and robust/resistant averaging weights based on values of |zi| = |Δi|/max{σmedian, |Δ|median[n/(n−1)]1/2}. For outlier discrimination or down-weighting, sample median values have the advantage of being much less outlier-based than sample mean values would be.