The Standard Deviation is a measure of the spread of scores within a set of data. Mostly, we want to know about the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. These two standard deviations sample and population standard deviations are calculated differently.
The standard deviation measure variability and consistency of the sample or population. In most real-world applications, consistency is a great advantage. In statistical data analysis, less variation is often better.
In the picture below are the formulas of Population standard deviation and sample standard deviation.
Most of the people are keen about knowing the population standard deviation because our population contains all the values we are interested in. Therefore, you can calculate the population standard deviation if you have the entire population or you have a sample of a larger population.
Sometimes certain confusions are arisen as to which standard deviation should be used due to the name “sample” standard deviation incorrectly understood as meaning the standard deviation of the sample itself and not the estimate of the population standard deviation based on the sample.