Statistics Calculator
Comprehensive collection of statistical calculations for data analysis, risk and probability
Descriptive Statistics
Geometric Mean
Average for relative changes and growth rates
Harmonic Mean
Average for rates and ratios
Log Geometric Mean
Logarithmic geometric mean for logarithmic scales
Contraharmonic Mean
Specialized mean for certain data types
Mode
Most frequent value in a data series
Five-Number Summary
Min, Q1, Median, Q3, Max - distribution overview
Minimum and Maximum
Calculate Min, Max, and Range
Percentile
Percentiles and related statistical measures
Dispersion Measures
Pooled Variance
Combined variance of two samples
Pooled Standard Deviation
Combined standard deviation from multiple samples
Covariance
Joint variation of two variables
Skewness (g)
Asymmetry of distribution - skewness measurement
Kurtosis (κ)
Peakedness of distribution - kurtosis measurement
Distribution Functions
Distribution Function (CDF)
Empirical cumulative distribution function
Inverse Distribution Function
Inverse CDF - quantile function
Risk & Probability
Log Binomial Coefficient
Logarithm of binomial coefficient - numerically stable
Birthday Paradox
Probability of shared birthdays - counterintuitive mathematics
Bayes Theorem
Conditional probability - Bayesian statistics
Central Limit Theorem
Distribution of sample means
Similarities and Deviations
Dice Coefficient
Similarity measure for sets
Jaccard Index
Jaccard similarity between finite sets
Hellinger Distance
Distance between probability distributions
Mean Absolute Error (MAE)
Average absolute deviation
Mean Squared Error (MSE)
Average of squared deviations
Sum of Absolute Difference (SAD)
Total deviation between datasets
Sum of Squared Difference (SSD)
Total variability around regression line
Beta Functions
Beta Function
Special function of mathematical analysis
Incomplete Beta Function
Regularized incomplete beta function
Inverse Beta Function
Inverse incomplete beta function
Error Functions
Erf - Error Function
Error integral in probability theory
Erfc - Complementary Error Function
1 - Erf(x) - complement of error function
Erfi - Inverse Error Function
Inverse function of error function
Erfci - Inverse Complementary Error Function
Inverse function of complementary error function
About Statistics
Statistics is the science of analyzing and interpreting data. Statistical calculations form the foundation for:
- Data Analysis - Understanding patterns
- Quality Control - Process optimization
- Risk Analysis - Decision making
- Epidemiology - Healthcare
- Finance - Portfolio analysis
- Machine Learning - Algorithms
Fundamental Statistical Concepts
Measures of Location
Mean: μ = Σx/n
Median: middle value
Median: middle value
Measures of Spread
Variance: σ² = Σ(x-μ)²/n
Std Dev: σ = √σ²
Std Dev: σ = √σ²
Probability
P(A) = Cases/Total
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A∩B)/P(B)
Error Measures
MAE = Σ|y-ŷ|/n
MSE = Σ(y-ŷ)²/n
MSE = Σ(y-ŷ)²/n
Tip: Use descriptive statistics for data exploration before applying inferential methods. Always check assumptions of your statistical tests.
Practical Application Examples
Quality Control
- Standard Deviation: Process spread
- Mean: Target deviation
- Quartiles: Tolerance limits
Finance
- Variance: Risk measurement
- Covariance: Correlation
- Probability: Value-at-Risk
Data Analysis
- Median: Robust tendency
- Skewness: Distribution shape
- Kurtosis: Extreme values
Machine Learning
- MSE: Model error measurement
- Binomial: Combinations
- Bayes: Classification
|
|
Quick Reference
μ = Σx/n
Mean
σ² = Σ(x-μ)²/n
Variance
σ = √σ²
Std Dev
P(A|B)
Conditional
C(n,k)
Binomial
|
|