Standard Deviation Calculator
Calculate standard deviation, variance, and mean for your data set. Supports both population and sample standard deviation calculations.
Population Standard Deviation
Sample Standard Deviation
Standard Deviation Formulas
Population Standard Deviation
Used when you have data for the entire population. Divides by N.
Sample Standard Deviation
Used when you have a sample from a larger population. Divides by n-1.
Variance
Variance is the square of standard deviation. Measures spread of data.
How to Use This Calculator
Choose Calculation Type
Select Population SD if you have data for the entire population, or Sample SD if you have a sample from a larger population.
Enter Your Data
Input your numbers separated by commas or spaces. You can enter as many values as needed.
Calculate Results
Click Calculate to get the count, mean, variance, and standard deviation for your data set.
Interpret Results
Review the calculated statistics. A higher standard deviation means data is more spread out from the mean.
Example Calculations
Test Scores
Calculate SD for test scores: 85, 90, 78, 92, 88
The scores are fairly consistent with low variation.
Product Weights
Weights in grams: 100, 102, 98, 101, 99, 103
Very consistent weights with minimal variation.
Sales Data
Daily sales: 50, 75, 60, 90, 55, 80, 70
Moderate variation in daily sales figures.
Where Standard Deviation Is Used
Finance & Investment
Measure investment risk and volatility. Higher SD indicates higher risk and potential returns in stock portfolios.
Quality Control
Monitor manufacturing consistency and product quality. Ensure products meet specifications with acceptable variation.
Education & Testing
Analyze test score distributions, grade curves, and student performance variability across classes and schools.
Healthcare & Medicine
Analyze patient data, clinical trial results, and medical measurements to assess treatment effectiveness and variability.
Data Science & Research
Fundamental statistical measure for data analysis, hypothesis testing, and understanding data distribution patterns.
Business Analytics
Analyze sales patterns, customer behavior, and operational metrics to identify trends and make data-driven decisions.
Frequently Asked Questions
What is standard deviation?
Standard deviation is a measure of how spread out numbers are from their average (mean). A low SD means data points are close to the mean, while a high SD means they're more spread out.
When should I use population vs sample SD?
Use population SD when you have data for the entire population. Use sample SD when you have a subset of data from a larger population. Sample SD uses n-1 (Bessel's correction) to provide an unbiased estimate.
What is the difference between variance and standard deviation?
Variance is the average of squared differences from the mean. Standard deviation is the square root of variance. SD is more commonly used because it's in the same units as the original data.
What does a high standard deviation mean?
A high standard deviation means data points are spread out over a wider range of values, indicating high variability or inconsistency. In finance, this often indicates higher risk.
Can standard deviation be negative?
No, standard deviation cannot be negative. It's always zero or positive because it's calculated from squared differences. A SD of zero means all values are identical.
How is standard deviation used in the 68-95-99.7 rule?
For normally distributed data, approximately 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. This is also called the empirical rule.