What is the Difference Between Population and Sample Standard Deviation?

The main difference between population and sample standard deviations lies in the data they are calculated from:

• Population Standard Deviation: This is a parameter, which is a fixed value calculated from every individual in the population. It measures the spread of data within an entire population and is typically used when you have access to all the data points in a population.
• Sample Standard Deviation: This is a statistic, meaning it is calculated from only some of the individuals in a population. It measures the spread of data within a sample representing a larger population and is typically used when you have access to only a part of the data points in a population.

The formulas for calculating population and sample standard deviations are similar, but there is a slight difference. When calculating the sample standard deviation, you divide by (n-1) instead of n, where n is the number of data points. This is because the sample standard deviation tends to underestimate the true variability in the population, and dividing by (n-1) corrects this bias.

In summary, use the population standard deviation when you have access to all the data points in a population, and use the sample standard deviation when you have access to only a part of the data points in a population.

Comparative Table: Population vs Sample Standard Deviation

The main difference between population and sample standard deviation lies in the data they describe and the formulas used to calculate them. Here is a comparison between the two:

The population standard deviation is calculated using the entire dataset, while the sample standard deviation is calculated using a subset of the data, called a sample. When calculating the sample standard deviation, the denominator uses $$n - 1$$ instead of $$N$$ to correct for the bias caused by estimating the true population standard deviation.