Comprehensive statistical analysis tools for descriptive statistics, probability distributions, hypothesis testing, and correlation analysis. Professional-grade calculations with detailed explanations and step-by-step solutions.
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Enter your data and click "Calculate Statistics" to see descriptive statistics results
Select distribution type, enter parameters and X value to calculate probability
Enter sample data and test parameters to perform hypothesis testing
Enter X and Y values to calculate correlation coefficient and perform regression analysis
Statistical Analysis Types
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Descriptive Statistics
Calculate mean, median, mode, standard deviation, variance, range, quartiles, and other summary statistics for your data set.
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Probability Distributions
Work with normal, binomial, and Poisson distributions. Calculate probabilities, percentiles, and critical values.
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Hypothesis Testing
Perform one-sample and two-sample t-tests, z-tests with automatic p-value calculation and statistical significance determination.
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Correlation & Regression
Calculate Pearson correlation coefficient, perform linear regression analysis, and determine relationship strength between variables.
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Data Validation
Automatic outlier detection, data normality testing, and input validation to ensure accurate statistical analysis.
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Detailed Explanations
Step-by-step calculations, formula explanations, and interpretation guidance for all statistical results.
How to Use the Statistics Calculator
📊 Descriptive Statistics Calculator
Enter your numerical data as comma-separated values to get comprehensive descriptive statistics including measures of central tendency, variability, and distribution shape.
Example: Test Scores Analysis
Input: 85, 90, 78, 92, 88, 85, 95, 82, 89, 91
Results: Mean = 87.5, Median = 88.5, Standard Deviation = 4.97, Range = 17
🎯 Probability Distribution Calculator
Select your distribution type and enter the appropriate parameters to calculate probabilities, cumulative distributions, and percentiles.
Example: Normal Distribution
Input: X = 100, μ = 95, σ = 5
Results: P(X ≤ 100) = 0.8413, Z-score = 1.0
🧪 Hypothesis Testing Calculator
Input your sample data and null hypothesis parameters to perform statistical tests and determine significance.
Our calculator uses industry-standard statistical formulas with double-precision floating-point arithmetic, providing accuracy to 15 decimal places. Results are mathematically equivalent to those from professional statistical software like SPSS or R.
What's the difference between population and sample statistics?
Population statistics describe the entire group you're studying, while sample statistics describe a subset. Our calculator defaults to sample statistics (using n-1 in denominator for variance) unless you're analyzing a complete population.
How do I interpret correlation coefficients?
Correlation coefficients range from -1 to +1. Values near 0 indicate weak correlation, while values near ±1 indicate strong correlation. Positive values show variables increase together, negative values show one increases as the other decreases.
When should I use a t-test vs z-test?
Use a t-test when the population standard deviation is unknown and you're using sample standard deviation (most common). Use a z-test when the population standard deviation is known or when sample size is very large (n > 30).
What does a p-value really mean?
The p-value is the probability of observing your results (or more extreme) if the null hypothesis were true. A small p-value (typically < 0.05) suggests your results are unlikely under the null hypothesis, leading to its rejection.
How many data points do I need for reliable statistics?
For basic descriptive statistics, any amount helps, but for inferential statistics, aim for at least 30 data points. For hypothesis testing, power analysis can help determine optimal sample size based on expected effect size.
Can I use this calculator for my research or academic work?
Yes! Our calculator is suitable for academic research, business analysis, and scientific studies. However, for critical research, we recommend verifying results with dedicated statistical software and consulting with a statistician.
What should I do if my data doesn't meet test assumptions?
If your data violates assumptions (like normality), consider data transformation, non-parametric alternatives, or robust statistical methods. Our calculator includes guidance on when assumptions might be violated.
How do I handle outliers in my statistical analysis?
Outliers can significantly affect results. Options include: investigating the cause, using robust statistics, transforming data, or reporting results both with and without outliers. Never simply delete outliers without justification.
What's the difference between Type I and Type II errors?
Type I error (α) is rejecting a true null hypothesis (false positive). Type II error (β) is failing to reject a false null hypothesis (false negative). Power = 1 - β is the probability of correctly rejecting a false null hypothesis.
About This Statistics Calculator
Our comprehensive Statistics Calculator is designed to make statistical analysis accessible to students, researchers, business analysts, and professionals across all fields. Whether you're conducting academic research, analyzing business data, or learning statistics, this tool provides accurate calculations with detailed explanations.
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Professional Accuracy
Industry-standard algorithms ensure results match those from SPSS, R, and other professional statistical software.
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Educational Value
Step-by-step calculations and formula explanations help you understand the statistical concepts behind each result.
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Privacy First
All calculations are performed locally in your browser. Your data never leaves your device, ensuring complete privacy.
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Mobile Optimized
Responsive design works perfectly on desktops, tablets, and smartphones for analysis anywhere, anytime.
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Instant Results
Real-time calculations provide immediate feedback as you enter data, enabling rapid statistical exploration.
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Always Free
Full access to all statistical functions without registration, subscriptions, or hidden costs.
Disclaimer: While our calculator provides accurate statistical computations using standard formulas, it should not replace professional statistical consultation for critical research or business decisions. Always verify important results and consider the assumptions underlying each statistical test.