I have generated a vector of data 'y' from a symmetric distribution (let's assume the Normal distribution). I have used R language for generating the data:
x = seq(60, 80, 0.01); y = dnorm(x, mean=70, sd=1); z = skewness(y);
z = 2.18358
Shouldn't I get 'z' equal to zero or very near to zero?
I have also increased the sampling rate from 0.01 to 0.0001 to 0.0000001 and got z from 2.18358 to 2.182749 to 2.182741. The same occurs with many other symmetric distributions that I have tested.