Standard Deviation Calculator - Free Online Statistics Tool
Calculate standard deviation, variance, mean, confidence intervals, and comprehensive statistical analysis instantly. Advanced calculator with population and sample modes, quartiles, outliers detection, and detailed distribution analysis.
Separate numbers with commas, spaces, or new lines. Supports grouped data, ungrouped data, frequency distribution, test scores, stock prices, investment returns, scientific data, research data, survey data, experimental data, financial data, business data, medical data, engineering data, social science data, educational data, psychological data, environmental data, quality control data, process data, performance data, marketing data, sales data, customer data, analytics data.
How to Use Standard Deviation Calculator
Step-by-Step Instructions
- 1Enter your data points separated by commas, spaces, or new lines
- 2Choose between Population or Sample standard deviation
- 3Select your desired confidence level (90%, 95%, or 99%)
- 4Click "Calculate Statistics" to get comprehensive results
- 5Explore detailed statistics across multiple tabs
Example Input
10, 12, 23, 23, 16, 23, 21, 16
This will calculate standard deviation, variance, mean, and other statistics
Advanced Features
Statistical Measures
- Mean, Median, and Mode calculation
- Standard Deviation (Population & Sample)
- Variance and Range analysis
- Coefficient of Variation
- Skewness and Kurtosis
Advanced Analysis
- Quartiles and IQR calculation
- Outliers detection and analysis
- Confidence Intervals (90%, 95%, 99%)
- Z-scores and Percentiles
- Distribution analysis
Common Use Cases
Academic & Research
- Statistical analysis for research papers
- Quality control in manufacturing
- Financial risk assessment
- Market research and surveys
Professional Applications
- Data science and analytics
- Performance measurement
- Investment portfolio analysis
- Scientific experiments and trials
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation uses N in the denominator and is used when you have data for the entire population. Sample standard deviation uses N-1 in the denominator and is used when you have a sample from a larger population. The sample standard deviation provides a better estimate of the population parameter.
How do I interpret the confidence interval?
A confidence interval provides a range of values within which the true population mean is likely to fall. For example, a 95% confidence interval means we are 95% confident that the true mean lies within the calculated range.
What do outliers indicate in my data?
Outliers are data points that fall significantly outside the normal range of your dataset. They can indicate measurement errors, special conditions, or important variations that need further investigation.
What is the coefficient of variation and why is it useful?
The coefficient of variation (CV) is the ratio of standard deviation to mean, expressed as a percentage. It's useful for comparing the relative variability of datasets with different units or scales.
Can I export my calculation results?
Yes! You can export your results in JSON format or copy individual values to your clipboard. The calculator also maintains a history of your recent calculations for easy reference.