Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution:
- numbers 1, 2 and 3 about 20 occurrences
- number 6 has 2 occurrences and
- number 9 has only one occurrence
I want to calculate "coefficient of uniformity of the distribution" (sorry I named this), or a kind of "properly adjusted min-max for the interval", which need not to be 1 to 9 (the obvious min-max), but to be kind of "centered" only around the most frequently occurring values (1,2 и 3) In this particular example, such adjusted (mean) interval would be roughly from 1 to 5 - Despite there are the extreme values of 6 and 9, because they are rare compared to 1, 2 and 3, so that they do not stretch the interval that much to include them. I know it is something from Statistics but I lack the theoretical details. Hint to some traditional method of calculating such kind of "mean distribution" interval from a given set of numbers?
EDIT: Do you think a form of amplifying-abbreviating would do what I want? I got an idea that I can apply some linear amplification of the data set by some multiplier (choose the multiplier so that I get the level of distribution which I want within the original min-max), and then abbreviate by the same multiplier both the dataset and the min-max of the absolute interval altogether, this way I render the extremes which I do not want as clipping, and still cover this so wanted statistically significant part of my dataset within my desired fixed min-max. I forgot to mention that ultimately I have to do a fixed interval transformation of the dataset. (const -1, 1) and wish to clip outside this range those nasty extremes, but I have to determine all of this automatically, cause I know nothing about the dataset's uniformity in advance. Actually this is the main problem :(
This lefts me yet one unknown. How to determine when satisfying distribution saturation within the original min-max is reached? I imagine I can make a bubble like looping algo of amplifying and re-testing some kind of "indicator of uniformity" repeatedly until I get the desired saturation. Somebody know of such indicator a calculated number that I can compare by given by me constant ?