we learned that sample variance is an unbiased estimator for the population variance when:
- sampling with replacement;
- we make all possible samples from the population. If we don`t it is not an unbiased estimator.
How can we use it in practice?
In my opinion, when an estimator is unbiased, you can use samples to estimate properties of the population. The population may be very large and it would be very costly and time consuming to measure the entire population.
For example, if you are trying to estimate for underweight or overweight of a product in a production facility and the number of products produced per day is 1 million. Since it is not possible to weight everything, you will take measurements at some time intervals. And you will do so from some number of samples that is a certain percentage of the population size.
When you make your estimation with the unbiased estimator, you are almost certain not to be far from what you will get if you did this experiment on the entire population.