# What is the difference between population standard deviation, sample standard deviation, and standard error?

Sorry for the rudimentary question, but I just want to make sure I understand everything well conceptually. I understand how we get the standard deviation of a population. My questions are as follows:

1. If we want to describe the spread of a sample of data, why would we not use the same formula we would for the population? In other words, given a population of 20 individuals and a sample of 20 individuals, why don't we divide by N for both of the data sets to express how far on average each data point is from each sample's mean? Given all data points are the same, wouldn't these two necessarily have the same spread, and therefore should have the same numerical value for a measure of spread (standard deviation)?

2. Can one use the sample standard deviation to estimate the population standard deviation? Is this when the N vs. n-1 question comes into play?

3. Standard error tells us how far, on average, a given sample mean deviates from the true mean of these means (which will be the population mean), correct?

• Please check the site for possible duplicates. I think you will find that this has already been answered. – Michael R. Chernick Nov 28 '19 at 20:37