Why non-zero skewness is obtained from symmetric probability distribution?

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);


Result:

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.

• That's not how you generate a random sample from the normal distribution. It's the function rnormyou have to use. What you have done is just compute values of the density function at regular intervals. Those indeed form a skewed set of values. – Raskolnikov Nov 17 '17 at 7:00
• @Raskolnikov You are right. I was mistaken. – MM Khan Nov 17 '17 at 10:27