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When applying the Empirical formula on a data set, for example calculating 1, 2 or 3 standard deviations below and above the mean of a data set, for some cases, this might not make sense. For example, when dealing with data of time, is it acceptable to say:

$mean - (2 * s.d.) = -5$ hours?

Or does this truncate to $0$ hours?

Thanks for any insight!

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Occasionally when a quantity, say time $t$, is constrained to be positive, it might make more sense to talk about the standard deviation of $\log t$. Then this would give you confidence intervals in the region $t > 0$. –  Trevor Wilson Sep 5 '12 at 2:34
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up vote 1 down vote accepted

The empirical rule applies to the normal distribution and not generally. It can be a useful approximate rule for distributions whose shape is close to the normal. But it would not apply to highly skewed or very heavytailed distributions. The Chebyshev inequality provides general bounds that apply to all distributions with finite variances.

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