So i have a dataset that tracks widget production from 100 different factories, each individually owned and highly competitive. Each line contains the factory name, the date of production, and the # of widgets produced.
As expected, some widget factories produce way more widgets than others. In fact, the top few factories typically account for 70% of widget production.
I am the government and hold and see all of this data, but no individual widget factory has all of the data. However, I would like to provide "aggregate" statistics to all widget producers such that they can compare their own factory's performance to the "industry average".
However, I cannot do a simple weighted average, as this would expose the growth rate of the top few factories. Down-weighting the top producers will give me growth rates that correlate with the "total" widget growth rate, but would not have the same magnitude, so I don’t think that number is particularly useful.
What are typical solutions to this issue? I want to show an accurate % change in total industry widget production from week to week, but don't want to put anyone at a disadvantage. This seems like a problem the bureau of labor statistics would run into frequently, for example if they are posting monthly manufacturing data and certain sectors only have a small number of primary contributors to those numbers. Would do they do in these scenarios? How are they "anonymizing" the data while still making it useful?