Yes, it is a common misconception that SD simply goes down as sample size goes up, but really as sample size increases what you actually get is a better a estimate of the true variation (dispersion) within a population.
Graph below is the SD of a population as sample size increases.
Once the sample size is large enough, the SD stays approximately constant. Indeed, the fact that SD becomes a constant over a certain sample size is why it is useful. SD describes the spread of the population.
Let’s look at a different term you will have likely heard about… standard error of the mean (SEM). How does SEM relate to SD?
LaNts and Laminins 