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I've been using relative standard deviation as a measure of variance for my variables, but some of them take both positive and negative values and their mean is close to zero, so it's not a good indicator of variance anymore. Are there any alternatives?

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Now, your relative standard deviation (RSD) indicates whether the normal standard deviation is a small or large after being divided by the mean of the data set.

My suggestion, as the mean may be going 'negative' in the context of your data, since the mean is sensitive to outliers. The latter could include an occasional large negative value. So, consider a more robust measure of central location, like the median.

For dispersion, compute the average of the absolute value of an observation minus the median over the data set.

Note, both parameters are consistent with assuming the parent distribution is Laplace (see Wikipedia).

You can now compute the corresponding statistic, which relates to the relative average deviation for the data set, which indicates how each measurement relatively differs from the central point (median) of the data set (where the median of your data may likely not ever be negative).

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