I entered the following command in R:
my_pois <- replicate(100,rpois(5,10))
[1] 10.8 9.4 9.0 11.2 11.6 11.6 7.8 12.4 9.6 11.0 9.6 9.8 10.0 8.6 9.8 8.6 9.4
[18] 11.4 12.0 8.4 10.2 10.2 10.8 10.2 7.6 9.8 8.4 10.6 11.6 8.6 9.6 11.0 11.0 10.0
[35] 9.8 9.2 8.2 8.2 10.2 9.0 10.4 9.2 10.4 10.0 11.8 13.8 10.2 9.8 12.4 10.4 9.8
[52] 9.8 8.6 7.4 9.2 9.0 7.4 9.2 9.4 11.8 9.2 9.8 11.6 9.8 10.8 8.6 12.4 10.4
[69] 9.4 9.4 9.0 11.2 10.6 9.4 9.6 8.2 9.6 10.6 10.6 8.2 9.2 10.0 11.2 9.0 9.6
[86] 10.4 8.0 10.2 9.8 7.4 9.6 9.0 7.2 8.4 11.8 10.8 9.4 12.4 11.2 12.0
You can calculate the mean of all the samples using the following.
k <- apply(my_pois,2, function(x) mean(x))
You are creating a random sample which should be approximately equal to 10. Since your sample is small it is unlikely to equal 10 exactly. As your sample size grows the mean comes closer to 10.
Here is one source I would review