Browse Formulas by Category
Master statistics with our comprehensive collection of formulas covering descriptive statistics, probability distributions, hypothesis testing, regression analysis, and advanced statistical methods. From basic mean and standard deviation to complex multivariate analysis, find every formula you need with detailed explanations and real-world applications.
Set
Learn the concept of sets in statistics and mathematics with proper notation and classification. Foundational for probability.
- Basic Set Definition and Notation
- Types of Sets
- Set Relationships and Comparisons
- Cardinality and Set Size
- Universal Set and Complement
- Basic Set Operations
- Set Algebra Laws
- Cartesian Product and Ordered Pairs
- Power Set
- Inclusion-Exclusion Principle
- Special Sets in Mathematics
- Set Construction Methods
Subset
Understand what a subset is, its types, and how to identify subsets of given sets. Essential for set theory and probability.
- Basic Subset Definition
- Proper Subset Definition
- Types of Subsets
- Number of Subsets (Cardinality)
- Properties of Subset Relation
- Special Subset Relationships
- Subset and Set Operations
- Power Set and Subsets
- Subset Chains and Hierarchies
- Subset Testing and Verification
- Subset Lattice Structure
- Subset Enumeration and Generation
Intersection
Explore how to find the intersection of sets using Venn diagrams and formulas. Useful in probability and logic.
Union
Learn how to calculate the union of two or more sets using standard formulas and diagrams.
- Basic Definition of Union
- Extended union operations
- Fundamental Properties of Union
- Absorption and Domination Laws
- Distributive Laws
- De Morgan's Laws for Union
- Cardinality and Inclusion-Exclusion
- Union with Special Sets
- Monotonicity Properties
- Infinite Unions and Limits
- Disjoint Unions and Partitions
- Union in Different Mathematical Contexts
Relative Complement of A in B
Understand the relative complement of set A in B and how to compute it using Venn diagrams and examples.
- Basic Definition of Set Difference
- Alternative Notations and Representations
- Basic Properties of Set Difference
- Relationship with Other Set Operations
- Distributive Laws for Set Difference
- Special Cases and Identity Elements
- Cardinality and Set Difference
- Multiple Set Differences
- Complement vs. Relative Complement
- De Morgan-style Laws for Difference
Absolute Complement
Learn about absolute complement of a set relative to a universal set, including notation and examples.
Symmetric Difference
Explore symmetric difference between sets, defined as elements in either A or B but not both.
- Basic Definition of Symmetric Difference
- Alternative Representations
- Fundamental Properties
- Relationship with Other Operations
- Advanced Algebraic Properties
- Cardinality and Size Relationships
- Involution and Inverse Properties
- Boolean Algebra and XOR Connection
- Multiple Set Symmetric Difference
- Symmetric Difference in Vector Spaces
- Distance and Metric Properties
Operations On Sets
Understand key set operations including union, intersection, complement, and difference. Visualize with Venn diagrams.
- Union Operation
- Intersection Operation
- Difference Operation
- Symmetric Difference Operation
- Complement Operation
- Double Complement Operation
- Cartesian Product Operation
- Commutative Properties
- Associative Properties
- Distributive Laws
- De Morgan's Laws
- Identity and Special Elements
- Cardinality and Operations
Combinations
Learn combination formulas to find how many ways items can be selected without regard to order.
Permutations
Understand permutation formulas used to calculate arrangements where order matters. Includes nPr formula.
Probability
Explore basic probability formulas, definitions, and examples. Learn how to calculate outcomes and events.
Mean
Learn how to calculate the mean (average) of a dataset. Includes arithmetic mean formula and examples.
Median
Understand how to find the median, or middle value, of a sorted dataset. Includes examples and formulas.
Mode
Explore how to identify the mode, or most frequent value, in a dataset. Useful for frequency analysis.
Example
See a worked-out example applying key statistical formulas like mean, variance, and standard deviation.
Geometric Mean
Learn the formula and use of geometric mean to find central tendency in multiplicative data.
Harmonic Mean
Understand harmonic mean and its applications in statistics where rates or ratios are involved.
Variance
Calculate variance to understand how data points deviate from the mean. Includes formulas for population and sample variance.
- Population Variance
- Sample Variance
- Computational Formula
- Interpretation and Meaning
- Properties of Variance
- Variance of Independent Variables
- Variance Decomposition
- Pooled Variance
- Covariance and Correlation
- Variance of Common Distributions
- Variance Estimation and Inference
- Computational Considerations
Standard Deviation
Learn how to compute standard deviation to measure the spread of values in a dataset. Essential in statistics.
- Population Standard Deviation
- Sample Standard Deviation
- Computational Formula (Alternative)
- Interpretation and Meaning
- Empirical Rules and Guidelines
- Properties of Standard Deviation
- Standardization and Z-Scores
- Coefficient of Variation
- Pooled Standard Deviation
- Standard Error vs Standard Deviation
- Standard Deviation for Common Distributions
Root Mean Square
Understand the root mean square (RMS) and how to apply it in statistics, physics, and engineering.
Normal Distribution(gaussion Distribution)
Learn about the normal distribution, also known as the Gaussian distribution, including its properties and real-world applications.
- Probability Density Function
- Key Parameters and Moments
- Cumulative Distribution Function (CDF)
- Key Properties
- Common Distribution Examples
- Standardization and Z-Scores
- Empirical Rule (68-95-99.7 Rule)
- Properties and Characteristics
- Linear Combinations and Transformations
- Central Limit Theorem
- Probability Calculations
Exponential Distribution
Explore the exponential distribution used to model time between events in a Poisson process.
Poisson Distribution
Understand the Poisson distribution used for modeling count data and rare events in fixed intervals.
Uniforn Distribution
Learn about the uniform distribution where all outcomes are equally likely. Includes continuous and discrete forms.
- Continuous Uniform Distribution
- Cumulative Distribution Function
- Discrete Uniform Distribution
- Probability Density Function
- Key Properties
- Parameters and Moments
- Moments and Parameters
- Discrete Uniform Moments
- Properties and Characteristics
- Transformations and Relationships
- Order Statistics
- Random Number Generation
- Geometric and Trigonometric Applications
- Special Cases and Variants
- Parameter Estimation
Why Choose Our Math Formula Collection?
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Over 400 formulas across all major mathematical disciplines
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Whether you're preparing for an exam, solving real-world problems, or just brushing up on your skills, our formula collection is designed to make learning math intuitive and efficient.
๐ Bookmark This PageEssential Statistics Concepts
๐ Data Description
Master measures of central tendency, variability, and distribution shape to effectively summarize and describe data.
๐ฒ Probability Theory
Understand probability distributions, random variables, and the mathematical foundation of statistical inference.
๐ฌ Statistical Inference
Learn hypothesis testing, confidence intervals, and how to make decisions based on sample data.
๐ Predictive Modeling
Apply regression analysis, forecasting, and machine learning techniques to predict future outcomes.
Statistics Study Tips
Start with Descriptive Statistics
Master mean, median, mode, and standard deviation before moving to probability and inferential statistics.
Understand the Logic of Inference
Focus on the conceptual understanding of p-values, confidence intervals, and hypothesis testing logic.
Practice with Real Data
Work with actual datasets from your field of interest to see how statistics applies to real-world problems.
Learn Statistical Software
Master tools like R, Python, SPSS, or Excel to efficiently perform calculations and create visualizations.
Real-World Applications
Medical & Healthcare
Clinical trial design, epidemiological studies, biostatistics, survival analysis, and evidence-based medicine research.
Business & Economics
Market research, quality control, financial analysis, risk management, A/B testing, and business intelligence.
Scientific Research
Experimental design, data analysis, hypothesis testing, peer review studies, and reproducible research methods.
Manufacturing & Engineering
Six Sigma, process control, reliability analysis, design of experiments, and continuous improvement programs.
Quick Reference Guide
Statistics is the science of collecting, analyzing, interpreting, and presenting data. It provides the mathematical foundation for making informed decisions under uncertainty. Whether you're conducting research, analyzing business performance, testing hypotheses, or predicting future trends, statistics offers the tools and techniques to extract meaningful insights from data and quantify the reliability of your conclusions.