# Math Help - Sampling question

1. ## Sampling question

If N variables are normally distributed with the same mean and standard deviation, the true variance in the means among the N variables is zero. However, if the mean of each N_i is estimated from n samples, the estimated variance in the means among the N variables will be non-zero. What will the estimated variance be?

2. Originally Posted by ecotheory
If N variables are normally distributed with the same mean and standard deviation, the true variance in the means among the N variables is zero. However, if the mean of each N_i is estimated from n samples, the estimated variance in the means among the N variables will be non-zero. What will the estimated variance be?

var(N_1)/sqrt(n)

RonL

3. Thanks captain, but could you either generalize to more than one N_i, or offer a hint of explanation for your answer so that I might? I guess I should have specified that the true variance of each N_i is also estimated from the samples.