# How to convert mean and standard deviation to a single meaningful and quantifiable value?

I look at mean and standard deviation of various map like data and each give meaningful information but sometimes they provide different information.

For example, let's take states in a country. One state has higher mean than others but the standard deviation by itself looks OK since individual points from the whole state tend to be higher. In another case, the mean looks average but the state has both higher and lower values equally distributed so the standard deviation is higher.

Now how can you quantify both mean and standard deviation to a single meaningful value? Let say, the map color looks hot both when mean of each state is deviating from the mean of the country as well as standard deviation of the state is high.

• You can certainly turn state means into a $z$-score (or something loosely analogous, in your suggestion), but this does not address the additional information in each state's SD (assuming there is). If there is independent info in the state SDs, that will need to be represented somehow in addition. – gung - Reinstate Monica Apr 16 '14 at 18:05