# How to judge skewness based on the mean and range?

Is there any rule of thumb to judging skewness of data based on its mean and range (max-min)? I found such implication in one of the papers I'm reading and I can't see why it would be obvious.

The level of the mean and the range (maximum – minimum) suggests that the price levels are right-skewed. - http://essay.utwente.nl/60867/, page 48.

• Strange. Can you provide the title or a link to the paper? – Jon Nov 20 '16 at 20:26
• They probably mean just that the mean lies to the left of the centerpoint of the range interval. – kjetil b halvorsen Nov 21 '16 at 3:24
• Presumably like @kjetilbhalvorsen I guess that the implication is that the maximum and minimum are known. They are not just looking at its difference. It's the ambiguity, which doesn't often bite, between (a) the range as the interval from the minimum to the maximum and (b) the range as the difference between the maximum and the minimum. Remember that many non-mathematicians (and I'm one of them too) are liable to write the minus sign as equivalent to as dash and meaning "and". I've not followed up the link, as questions here should be self-contained. – Nick Cox Nov 21 '16 at 10:59
• Thank you all! It seems that there's nothing deep in this statement and it's mainly about where the mean is compared to min and max. – Paula Nov 21 '16 at 19:09
• The main problem is that in any symmetric (non-skewed) continuous distribution, the mean is certain not to lie midway between the min and the max. Even worse, with many distributions having tapering tails--such as Normal, Gamma, lognormal, Weibull, and many more forms commonly encountered in data--one or both of the min and max is so extremely variable that using it to draw any kind of conclusion is about the riskiest way one can find to analyze the data. – whuber Nov 21 '16 at 23:33