I am new in statistic. I come across the sample variance calculation in a book and it explains that denominator is divided by n-1 instead of n is because variance in samples will be likely to be lower than the population variance, so we divide by n-1 to make the variance larger. However, when I studied t-distribution, with small n, the distribution has fat tail. With larger n, the tail of distribution becomes thinner. So it seems like with small n, it has larger variance. If I treat small n as the case of the sampling above, the value of variance seems to contradict each other (first case states it would be smaller and second case states it would be larger). Could someone help me with this? Thanks.