One of the metrics in statistics is the standard deviation. When conducting research, the standard deviation is crucial for describing the data you have obtained. It illustrates the dispersion of the data relative to the mean.
The size of the standard deviation indicates the variation in the data you have collected. If the calculation results in a small standard deviation, it means the data points are clustered close to the mean. Conversely, a large standard deviation indicates that the data points are widely spread out from the mean.
Standard Deviation for Sample Data
It’s important to understand that standard deviation can be calculated in two ways: for population data and for sample data. Researchers will often calculate the standard deviation for sample data.
In research, we can take a representative sample from the observed population. Therefore, it is essential to understand the standard deviation of sample data thoroughly.
There is a slight difference between the calculation methods for the standard deviation of population data and sample data. In this article, I will provide a tutorial on how to find the standard deviation of sample data using Excel.
However, before proceeding to Excel, I will explain how to calculate it manually so that we can compare the results of manual calculations with the automated results obtained from Excel.
Formula for the Standard Deviation of Sample Data
As mentioned earlier, the formula for the standard deviation of sample data differs slightly from that for population data. The formula for calculating the standard deviation of sample data is as follows:
Case Study Example
For practice in calculating the standard deviation of sample data, I have prepared an example data sheet of income variables from a region (in millions of dollars). The data can be seen in the table below:
Manual Calculation of Standard Deviation for Sample Data
Based on the table above, the next step is to apply the formula to calculate the standard deviation of sample data. To simplify the calculation, the first step is to calculate the mean.
The mean can be calculated using the following formula:
Based on this formula, we can calculate the mean by creating a helper table in Excel. The next step is to calculate the difference between each observation and the mean, then square these differences.
After obtaining the sum of these squared differences, we take the square root. The detailed calculation results can be seen in the table below:
Based on the calculation, the standard deviation of the sample data is found to be 22.33.
Obtaining the Standard Deviation of Sample Data in Excel
Did you know? Excel also provides a built-in function to calculate the standard deviation of sample data. We can use the following formula in Excel to obtain the standard deviation:
=STDEV.S(sort all data)
By correctly and accurately entering the formula, Excel will display the standard deviation of the sample data, as shown in the image below:
Cross-Checking the Calculation Results
Now, let’s compare the results of our manual calculations with the automated results from Excel. The comparison can be seen in the image below:
Based on the image, it is evident that the results of the manual calculation using the sample data standard deviation formula and the automated calculation in Excel are exactly the same.
Thus, our calculations are accurate and correct. This means we can either calculate manually or directly use the formula in Excel to obtain the standard deviation of sample data.
Well, that concludes the article I’ve written for this occasion. I hope it is useful and provides new insights for those who need assistance in calculating the standard deviation of their research data. Thank you for reading this article to the very end, and stay tuned for updates from Kanda Data in the coming weeks. Thank you.
