I was thinking about z-scores and I'm curious about their usage when data are skewed/non-normal. I often see zscores being used to identify outliers, e.g. with z>1.96, 2.58, etc. HOWEVER: the z-score calculation of z = (x - mean(x)) / stdev(x) is dependent on the mean, and the mean is not an appropriate measure of central tendency when data are skewed. So when data are skewed, I think it's inappropriate to use z-scores and instead we should favour an alternative like Tukey's classification (how boxplots define outliers, can't remember exactly what it's called). Is this correct?