Then made a plot of magnitude vs number of stars at that magnitude. This would have a shape due to the distribution of stars in the sky. I think such fine structure will be smaller than the error. But this needs to be given proper analysis. Suppose we consider a bunch of buckets spread out over a line catching random rain drops.
Differential linearity is a measure of the diameter of each bucket.
In our case, we are allowed a bucket of zero width. Integral linearity is a measure of the uniform spacing of the buckets. Thus bucket 23,567 should be within 16 positions of its specified position. This means that all the buckets in between 1 and 23,567 have to be stretched or squished so that no two adjacent buckets are of zero width or more that twice their average diameter. One can have regions of wide and narrow buckets as long as no bucket is off by more than 16 positions.