# Solved – Quantiles for non-normal cdf

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?

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`summary(x)` is computing sample quantiles of your data, using type 7 quantiles (see `help(quantile)` in R for the various quantile types).
I'm guessing that you've used `summary(y)` to produce the second set of values. In that case, the results are probably not what you want as they are giving you quantiles of the data set {0,1,2,3,4,5,6}, the step points of the empirical cdf.
You can get the quantiles from the ecdf object using `quantile(y)` which should give you the same results as `quantile(x)`.