What are Population/Sample Variance, and Population/Sample standard Deviation for?

Question

Where do we use them in real life? How do they work?

Answer 1

The variance and the standard deviation are related.  The variance is just the standard deviation squared.  The variance tells you how spread out the data is of a sample.

For example, suppose I have two groups of people, and the average height of both groups of people is 5 feet tall.  Group A consists of people who are all exactly 5 feet tall.  Group B consists of infants and NBA basketball players.  The variance of the height of the people in Group B is large (the heights varied a lot), while the variance of the heights of group A was essentially zero (the heights did not vary at all).