Standard deviation is a crucial measure in explaining how data is distributed relative to its mean. Generally, when conducting research and performing descriptive statistical analysis, the value of the standard deviation will often appear.
Did you know that there is a difference between the standard deviation value for sample data and population data? Upon further investigation, it turns out that the difference lies in the formula used for the calculation.
Given the importance of calculating standard deviation, I am interested in writing an article discussing the differences between the standard deviation of population data and sample data. This is particularly relevant since most researchers, especially those observing large populations, often take a representative sample due to cost, time, and effort considerations. Before diving deeper into the differences in formulas, we first need to understand the distinction between populations and samples.
Differences Between Populations and Samples
Understanding the difference between populations and samples is essential for researchers. A population is the entirety of objects or individuals that are the focus of a study.
The boundaries of a population depend on the scope defined in the research. For example, if we aim to observe a variable in organic rice farmers in region ABC, then all farmers practicing organic farming in region ABC constitute the population of the study.
Meanwhile, a sample is a smaller subset of the population taken to represent the observed population. There are scientific principles that must be understood in sampling techniques to ensure that the selected sample is representative.
For instance, suppose there are 1,000 organic farmers in region ABC, and we take a sample of 200 farmers to represent the population. The sampling technique must adhere to scientific standards.
When observing a population, we measure parameters of the observed characteristics, whereas, in sample observation, we estimate those parameters using statistical approaches.
At this point, I hope readers have a good understanding of the differences between populations and samples. The next step is to understand the differences in the formulas for standard deviation between population data and sample data.
Differences in Standard Deviation Formulas for Population Data and Sample Data
Conceptually, the method for calculating standard deviation values for population data and sample data is nearly identical. Even the components used for assessment are the same. The difference lies in the divisor used in the standard deviation formula. The formula for calculating the standard deviation for population data is as follows:

Meanwhile, the formula for calculating the standard deviation for sample data is as follows:

Based on the formulas for calculating the standard deviation of population data and sample data, the difference lies in the divisor. In the standard deviation formula for population data, the divisor is N.
In contrast, the divisor in the standard deviation formula for sample data is n-1. Why is there a difference between the two?
As mentioned earlier, the sample is taken from the population using sampling techniques that adhere to scientific principles. Therefore, the standard deviation calculation for sample data needs to be corrected by dividing by n-1, often referred to as degrees of freedom.
Why is this necessary? When calculating the sample mean, one degree of freedom is lost because the mean itself is derived from the sample data. This adjustment ensures that the variance estimate is closer to the actual population and also avoids bias.
Additionally, it is important to understand that the symbols used in the formulas for standard deviation of population data and sample data differ. The standard deviation for population data is denoted by the symbol “σ” and for sample data by “s”. Similarly, the population mean is represented by “μ” and the sample mean by “x̅”.
Conclusion
Based on the discussion above, we can now distinguish the formulas used to calculate the standard deviation of population data and sample data. We also understand why the difference exists: the divisor n-1 in sample data is used to correct and reduce bias.
Additionally, it is worth noting that the standard deviation value for sample data is generally larger than that for population data. This is because the divisor n-1 is smaller.
This concludes the article I have written for now. I hope it is useful and adds value to those who need it. Stay tuned for updates from Kanda Data in future articles. Thank you!