Which Samples Underestimate the Population Standard Deviation?

The SD computed from tiny samples underestimate the population SD (but not by much) The standard deviation (SD) quantifies scatter.

Does the sample variance underestimate the population variance?

Source of Bias

In fact, pseudo-variance always underestimates the true sample variance (unless sample mean coincides with the population mean), as pseudo-mean is the minimizer of the pseudo-variance function as shown below.

Is standard deviation sample or population?

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability. Thus the standard deviation of the sample is greater than that of the population.