Standard Deviation Calculator
Calculate standard deviation and variance for a set of numbers. Perfect for statistics, data analysis, and measuring data spread.
The Standard Deviation Calculator helps you measure how much data values deviate from the mean. By entering your dataset and selecting either Population or Sample, the calculator computes the standard deviation instantly. Standard deviation is one of the most widely used measures of variability in statistics, finance, science, and research. A small standard deviation means values are close to the mean, while a large one indicates greater spread. This tool is ideal for students, teachers, analysts, and professionals who need accurate insights into data consistency or volatility.
Enter your dataset values separated by commas (e.g., 12, 15, 18, 20, 25).
Choose “Population” if working with all data points, or “Sample” for a subset of data.
Common scenarios: (1) Analyze exam results to see how scores vary from the average; (2) Measure investment volatility in finance; (3) Understand variation in scientific experiments; (4) Use in quality control to check consistency in manufacturing data.
Population Standard Deviation: σ = √[ Σ(xᵢ − μ)² / N ] Sample Standard Deviation: s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
Population standard deviation
Sample standard deviation
Each individual data point
Population mean (average of all data)
Sample mean (average of sample data)
Total number of population values
Total number of sample values
Dataset = 12, 15, 18, 20, 25.
Choose “Population Standard Deviation”.
μ = (12+15+18+20+25)/5 = 18. Then σ = √[(36+9+0+4+49)/5] = √(98/5) = √19.6 ≈ 4.43.
Population Standard Deviation ≈ 4.43.
The population standard deviation is used when you have data for the entire population, while the sample standard deviation is used when you only have a subset of the data. The sample standard deviation is slightly larger to account for the uncertainty of not having the entire population. This calculator can calculate both types of standard deviation. You can choose which one to use based on your specific needs.
To enter your data, simply type in the numbers separated by commas or spaces. You can also copy and paste a list of numbers into the input field. The calculator will then use these numbers to calculate the standard deviation and variance. Make sure to only enter numeric values, as non-numeric characters will cause an error.
The variance is a measure of how spread out a set of numbers is, and it is calculated as the average of the squared differences from the mean. The standard deviation is the square root of the variance. In other words, the standard deviation is a measure of the amount of variation or dispersion of a set of values, and the variance is the square of that value. This calculator will give you both the standard deviation and variance for your data.
Yes, this calculator can handle large datasets. However, keep in mind that very large datasets may take a few seconds to process. It is also worth noting that the calculator has a limit on the number of values you can enter, so if you have an extremely large dataset, you may need to split it up into smaller chunks. For most users, though, the calculator should be able to handle their data with no issues.
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