Your explanation made it click for me immediately. Thank you !
Or if you define median as inverseCDF(50/100) then percentiles are just inverseCDF(percentile/100)
data series: index -> value
integrate to cdf: value -> density
invert monotonic: density -> value
With the median being the same thing as p50
Wouldn't that be 99 buckets?
No. It’s 100 buckets with 101 percentiles, from p0 to p100.
With p0 and p100 being buckets whose min() values (and in the case of p100, only value) are also the min() and max() value of the whole set.
The buckets are 1,…,100, with percentiles being their boundaries. Since the 0th and 100th percentile are insufficient to form an interval, we only practically use percentiles 1,…,99.