I'm trying to make the jump from the idea of a percentile, say, over the real number line (where the nth percentile is simply the position in which n% of data points are below it, and 100-n% are above it), to the idea of the area under a probability density function.
If I want to know the 50% percentile from a set of numbers, I'll find the point in which half the numbers are below, half the numbers are above. That's the 50% percentile, and I'm done.
If I want to know the 50% percentile from a distribution, say, a Z-score, I'll evaluate the cdf from 0 - 50, and I'm done. Am I saying this correct?
This feel right intuitively, but I need some discussion to hammer it home. Or, I could be completely off...