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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#### Best Answer

This has nothing to do with being non-normal.

`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)`

.