For a fixed memory budget, a histogram with per-bin means and half the bins can have lower information loss (by the paper's EMDCC metric) than a histogram with twice as many plain bins.
Monitoring networked applications with incre- mental quantile estimation,
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HistogramTools for Efficient Data Analysis and Distribution Representation in Large Data Sets
For a fixed memory budget, a histogram with per-bin means and half the bins can have lower information loss (by the paper's EMDCC metric) than a histogram with twice as many plain bins.