When I compute the five-number summary on my sample, I obtain quantiles that differ from the quantiles I got from the empirical cdf, since they are not normally distributed data.
Can you help me in the interpretation of this difference?
For instance, with a randomly-generated Poisson dataset x
x=rpois(50, 2) summary(x) Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00 1.00 1.50 1.82 2.75 6.00 y=ecdf(x) summary(y) Empirical CDF: 7 unique values with summary Min. 1st Qu. Median Mean 3rd Qu. Max. 0.0 1.5 3.0 3.0 4.5 6.0
What does it mean that the 3rd quantile of the sample is
2.75 while it is
4.5 for the ecdf?