randn function does not work

the average value of data generated by function 'randn' is not zero

[Stephen23]

It doesn't have to be. What would you expect for a random sample of one?

Answer 1

[Walter Roberson]

Any one call to randn() is a finite sampling of the infinite distribution. The mean of 0 is statistical, not guaranteed for any finite subset.

If it were otherwise, imagine doing randn(1,1): in order for the mean of that sampling to be 0 each randn(1,1) would have to return 0. For randn(1,2) with two values being generated, both would have to be 0 or the two would have to be exact negatives of each other.

You can do statistical modeling to figure out the probability of the mean of a finite sampling being more than any given value.

Answer 2

[Guillaume]

For some reason, my dice don't work either. I've thrown them many times, yet the mean value is not exactly 3.5.

 >> mean(randn(1, 1e8))
 ans  = 
    -1.9019e-04

Pretty close to zero if you ask me. You'll only get exactly zero if you call randn an infinite number of times (or you're really lucky)

Answer 3

[Binbin Zhang]

Thanks a lot, got it.

[David Goodmanson]

Somebody should mention that if you take N samples from a distribution with standard deviation 1, then the standard deviation of the N-sample mean is 1/sqrt(N). So in Guillaume's example with N = 1e8, you would expect an answer down around 1e-4, which is what happened.