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i'm trying to represent concentration/distribution across a set of categories.

Specifically these are job types, e.g. tourism, manufacturing, transport, education. Let's say there are 10 job types and 3 cities:

City 1: 100k jobs. All are in tourism. [highly concentrated]

City 2: 75k jobs, 91% in tourism, 1% in each of 9 other industries. [highly concentrated]

City 3: 30k jobs, 10% in each of 10 industries. [highly distributed]

I'm not a stats guy but this feels like it should be something obvious and i'm struggling to find it. i can't see how i could use stand dev as there is no mean.

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  • $\begingroup$ I don't understand what you mean when you say the distribution has no mean. It is certainly true that a distribution (e.g. the Cauchy) can have a non-finite mean (i.e. it is commonly said that the mean doesn't exist in such cases) and therefore the standard deviation also doesn't exist. I doubt that this is what you mean. $\endgroup$ – Michael R. Chernick Nov 5 at 21:36
  • $\begingroup$ Besides the indicated duplicates there are many questions on site relating to these measures and related keywords you can find in those posts and the linked articles. You may like to try a few searches. $\endgroup$ – Glen_b -Reinstate Monica Nov 5 at 22:49