How to Calculate Population Data Standard Deviation Using Excel

Standard deviation can be used to understand how data is distributed relative to its mean. Calculating the standard deviation in research is crucial because it determines the variability of the data.

The larger the standard deviation, the higher the variance. In regression analysis, for instance, higher variability may result in a smaller t-statistic. A smaller t-statistic makes it more challenging to reject the null hypothesis.

Given the importance of understanding how to calculate standard deviation, this article provides a tutorial on calculating the standard deviation for population data specifically. The calculation method for sample data has been discussed in a previous article, which you can search for on this website.

Formula for Calculating Population Data Standard Deviation

The formula for calculating the standard deviation of population data differs from that for sample data. The differences between the two formulas have also been covered in an article posted last week.

Before diving into the formula, it’s essential to understand the difference between population and sample data. Essentially, population data includes all observed objects. For example, if I observe income data for 25 regions in a country where the country consists of only those 25 regions, I am dealing with population data.

If I observe only a portion of the population, then I am working with sample data. Hopefully, this explanation helps clarify the distinction between population and sample data.

For population data, the divisor in the standard deviation formula is the total number of population members. The detailed formula for calculating the population data standard deviation is as follows:

Practice Material for Standard Deviation Calculation

To practice manual calculation of the population data standard deviation, I have prepared a sample case study. The provided data represents income figures in millions of US dollars for 25 regions in country ABC.

This data is purely for practice and does not represent actual data. The practice data can be found in the table below:

Steps to Calculate Population Data Standard Deviation

Next, we need to follow several steps to calculate the population data standard deviation. To make calculations easier, I will use Excel, which is widely used and understood.

Let’s revisit the standard deviation formula. Based on the formula, we need to create an auxiliary table containing all necessary components. In Excel, we can add two additional columns to facilitate the calculation. These columns are detailed in the table below:

From the table above and the formula, the first step is calculating the population data mean. The population mean is often denoted by the symbol “μ.” The formula to calculate the mean is to sum all the population data and divide the result by the total number of population members, represented by “N.”

In Excel, we can calculate the mean by typing the formula “=AVERAGE(select all data)”. Press Enter, and the mean value will appear.

The next step is calculating the first auxiliary column, which involves subtracting the actual observation values from the mean. In Excel, this can be easily done by typing a formula as you would in a standard mathematical operation.

Once you’ve calculated the value for the first observation, ensure you make the mean value cell absolute by pressing F4 on your keyboard before copying and pasting the formula for observations 2 through 25.

For the second auxiliary column, square the results from the first auxiliary column and copy the formula through to observation 25. Finally, sum all the values in this column by typing the formula “=SUM(select calculated data)”.

After pressing Enter, the total value will appear. Next, we look at the formula again to divide the summed value by N (where N = 25). Then, take the square root of the result.

The obtained value is the population data standard deviation. The detailed results of the calculations can be seen in the table below:

Cross-Checking Calculations with Mathematical Formulas

Congratulations on manually calculating the population data standard deviation! To ensure the accuracy of your results, you can use Excel’s automatic formula. Use the formula  “=STD.P(select all data)”.

Note that you need to be cautious when selecting the standard deviation formula in Excel, as there are options for both population and sample data. For population data, choose  “STD.P”. After typing the formula and selecting all data, the standard deviation will display as 43.47.

This confirms that the manual and automatic calculation results are identical, proving that our calculations are correct. That concludes this article. I hope it is beneficial and adds new insights for those learning this calculation. Thank you for your attention, and see you in the next Kanda Data article!