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I have a sample of about 400 natural numbers though I can get more numbers. To give you an idea the mean and the standard deviation are 29038031 and 1842882 respectively and I expect the numbers to follow a Gaussian distribution. I'd like to perform a test to tell me the probability that my sample is truly random. I just don't know which test to perform. I've read about diehard tests but I don't see how I could apply them.

So I'd like to hear some suggestions. Thanks!

Edit: 1st idea that I have: get more numbers. Then perform a Gaussian fit and calculate the residuals. Do the same for true random numbers following a Gaussian with the same mean and standard deviation and compare the residuals. I expect lower residuals with the true random numbers.

Edit2: Nevermind this idea would be useless. It would tell me how far from a Gaussian my distribution of numbers is, not how random they are...

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# Testing how much random is my sample

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