This calculator computes both population standard deviation (σ) and sample standard deviation (s) all in one place. You only need to enter the data, select between sample and population, and click the “calculate” button.
The calculator will instantly return the correct standard deviation, along with a clear step-by-step solution. The explanation includes all the necessary statistics (mean, n, sum of squared deviations) you need to calculate the standard deviation by hand.
Enter your data separated by commas, spaces, tabs or copy-paste from Excel.
How to Use the Standard Deviation Calculator
Calculating the standard deviation for population or sample data using the calculator is very simple. Just follow these steps:
- Enter the raw data and separate it either with commas, spaces, or tabs. You can also copy-paste from Excel.
- Select the type of standard deviation you wish to calculate (sample/population?).
- Click the “Calculate” button.
The calculator will return the correct standard deviation and show you how you’d apply the appropriate formula to get the correct value.
Thus, with this tool, you not only get accurate answers but also learn how to find the standard deviation by hand.
What is Standard Deviation?
Standard deviation is a statistical measure that tells you how spread out your data is from the average (mean). In simple terms, it shows whether your data is tightly clustered around the mean or widely scattered. A small standard deviation means your values are close together, while a larger one means there is more variability in your dataset.
There are two types of standard deviations:
- Population standard deviation, which tells you how spread out the population data is from the population mean.
- The sample standard deviation, which informs you how spread out the sample data is from the sample mean.
Want to learn more about population and sample standard deviation? Check out our population standard deviation calculator and sample standard deviation calculator. You’ll find details on how to calculate each of them using the calculator and by hand. You’ll also get worked-out examples to help you learn.
When to Use Population vs Sample Standard Deviation
Unsure whether to use population or sample standard deviation? Don’t worry! The choice depends on the type of data you’re working with. Here’s a quick summary to help you choose the right method:
- Use the population standard deviation if the data you’re working with includes every member in the group you’re studying.
- Use the sample standard deviation if the data you’re working with is a subset (sample) drawn from a larger group (population).
Want a quick overview of their differences? The following table shows a summary of the key differences between their formulas and use cases.
| Type | Formula | Use Case |
|---|---|---|
| Population | σ = √(Σ(x − μ)² / N) | Entire population |
| Sample | s = √(Σ(x − x̄)² / (n − 1)) | Subset of population |
Note. From the table, you’ll note that the key differences are in their formula. For population data, the sum of squared deviations is divided by N, whereas that of the sample is divided by n-1. The n-1 adjustment is known as Bessel’s correction and helps you get a more accurate estimate of the true population variability even when working with sample data.