David B. answered • 02/20/21
Tutor
5.0
(257)
Math and Statistics need not be scary
If I understand you, you have a piecewise distribution where you have the percentiles, then you have defined (roughly) the population distribution. You can calculate the mean using the standard function for expected value
E(X) = ∑ xi · P(xi). for all the values you have in your percentile list.
BTW , your example looks wrong. If the gap between each percentile is the same the last one would be 99 - x100, since you started at 0
David B.
Your confusion is in the definition of percentiles vs quantiles. Quantiles represent the CDF. Percentiles represent the amount in one of 100 'blocks' of values. Here is a definition (in math, always look to your definitions when starting a problem. The answer is almost always there. "As nouns the difference between quantile and percentile is that quantile is (statistics) one of the class of values of a variate which divides the members of a batch or sample into equal-sized subgroups of adjacent values or a probability distribution into distributions of equal probability while percentile is (statistics) any of the ninety-nine points that divide an ordered distribution into one hundred parts, each containing one per cent of the population."
Report
02/22/21
Dan V.
Yes, but since percentiles represent the CDF I don't have P(xi) for a certain score Xn, just ∑ P(xi) for i = [0,n]. Would that be correct or am I thinking about it wrong?02/21/21