# Solved – Standard deviation to describe variation in positively skewed data

normal distributionquantilesskewnessstandard deviation

I'm wondering how useful the standard deviation is when applied to positively skewed data? The standard deviation implies that 68% of data will lie within one standard deviation of the mean, but surely this will not work for positively skewed data? This page suggests that for positively skewed data, the standard deviation is not useful and quartiles should be used instead.

#### Best Answer

I'm wondering how useful the standard deviation is when applied to positively skewed data?

It can be quite useful but it depends on what you're doing.

For example, I use the lognormal and gamma distributions regularly and sometimes use the standard deviation with those distributions -- it can be informative in some contexts.

The standard deviation implies that 68% of data will lie within one standard deviation of the mean,

No, that's true for normal populations. It's not something that holds more generally - even with symmetric distributions you can have almost nothing, or anything up to 100% within one standard deviation of the mean.

but surely this will not work for positively skewed data?

Again, it depends on the distribution - you might get more or less than 68% with positively skewed or negatively skewed distributions.

This page suggests that for positively skewed data, the standard deviation is not useful and quartiles should be used instead.

It depends on what you're trying to do. Distributions needn't be skew for the standard deviation not to be suitable, and the standard deviation may be quite okay when distributions are skew.