The following describes what I'm trying to accomplish, but it's possible an alternative problem statement can describe my goal:
I want to
divide the following numbers into groups where the variances of the numbers within each group are not too large, and the differences between the averages of groups are not too small
compare the distribution obtained in the end with the "perfect" ones and see how "different" it is from being perfect.
Layman's explanation of goal
I'm trying to calculate income distribution, and determine the "income brackets" each population is in. The income bracket is supposed to be self-adjusting based on the input data.
My goal is to ultimately measure or calculate the difference between the income brackets. I assume there will be many brackets, and want to see how far "apart" each tier is.
Here is a sample of hourly income for a sample set of a population of 20, and a total income of 3587:
Population= 10 pop=2 population=5 population =3
10, 11,13,14,14,14,14,14,15,20, 40,50 ,90,91,92,93,94 999,999,900
How can I use mathematical concepts to group, sort and analyze data that acts like income distribution over a given population?
At the end of the calculation, I want to determine tiered income distribution, where a perfect distribution would look (something) like this
(each person makes $10 more per hour than the previous; total is 3587)
89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259, 269, 279
or this:
(evenly distributed groups of people make the same per hour)
(gaps between income groups is consistent and not "too far")
(income total is 3587)
99 99 99 129 129 129 159 159 159 199 199 199 229 229 229 269 269 269
Question
How should I analyze the population groups, and measure the gap in a way that will tell me how much is needed to make it more like the last two model sets listed above?
It may seem you are interested in cluster analysis, but the problem with real-life distributions is they are nearly continuous, and hence the straightforward clusterization won't apply.
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