@michuk said in #1:
> I did Further Mathematics at college and in our Advanced Statistics class we were taught about this thing called mean of population. They said the mean of two population samples of people cannot be the same even if the samples are from same population of things.
The mean of two population samples CANNOT be the same? That is obviously incorrect. Of course it CAN be the same -- in the end we are talking about stochastic matters. But your statement is even incorrect in a more fundamental sense. The sample mean of a random sample is an unbiased estimator of the population average. Therefore, the sample mean gets closer and closer to the population average when the sample gets bigger. If you take two very large random samples of chess players, the means of the two samples will be very close to each other because they both approach the same population average.
> In other words if you segregate chess players and calculate a Gaussian distribution with mean and standard deviations in two population samples you will always have a gap.
That's simply incorrect.
> I did Further Mathematics at college and in our Advanced Statistics class we were taught about this thing called mean of population. They said the mean of two population samples of people cannot be the same even if the samples are from same population of things.
The mean of two population samples CANNOT be the same? That is obviously incorrect. Of course it CAN be the same -- in the end we are talking about stochastic matters. But your statement is even incorrect in a more fundamental sense. The sample mean of a random sample is an unbiased estimator of the population average. Therefore, the sample mean gets closer and closer to the population average when the sample gets bigger. If you take two very large random samples of chess players, the means of the two samples will be very close to each other because they both approach the same population average.
> In other words if you segregate chess players and calculate a Gaussian distribution with mean and standard deviations in two population samples you will always have a gap.
That's simply incorrect.