Standard Deviation Calculator
Analyze data variability
Data Set
Use Population if you have data for the entire group. Use Sample if you only have a subset.
Understanding Data Spread
Standard deviation is one of the most important concepts in statistics. It tells you how "normal" or "abnormal" a data point is compared to the average. In a normal distribution (bell curve), 68% of data points fall within one standard deviation of the mean.
This tool is essential for students, researchers, and financial analysts who need to understand risk, volatility, and consistency in their data.
How to Use This Calculator
Enter your data set, separating numbers with commas (e.g., 5, 10, 15, 20)
Select whether your data represents a 'Population' or a 'Sample'
Click 'Calculate' to process the data
View the Mean (Average), Sum of Squares, Variance, and Standard Deviation
Check the step-by-step table to see how each deviation was calculated
Pro Tips
- •Ensure data points are separated correctly by commas
- •Use 'Sample' for surveys or scientific experiments where you test a small group
- •Use 'Population' only if you have data for every single member of the group
- •Look at the variance to understand the squared spread before the root is taken
- •Standard deviation is sensitive to outliers (extreme values) - check your data for errors
Sample Standard Deviation Formula
s = √[ Σ(x - x̄)² / (n - 1) ]Where:
s= Sample standard deviationΣ= Sum ofx= Each value in the data setx̄= Mean (average) of the data setn= Number of values in the sampleExample:
Data= 2, 4, 4, 4, 5, 5, 7, 9Mean (x̄)= 5n= 8Calculation:
√[ 30 / 7 ] = √4.2857Result: 2.07
Frequently Asked Questions
Population standard deviation (σ) is used when you have data for the entire group you're studying (e.g., ages of all students in a class). Sample standard deviation (s) is used when you only have a subset of the data (e.g., ages of 50 randomly selected people from a country). Sample SD divides by (n-1) instead of n to correct for bias.