Statistics
The numbers back it up: statistics doesn't have to be hard. Learn to explain data and calculate statistics with beginner to advanced tutorials, tools, worksheets, and formulas for students and teachers.

The Associative and Commutative Properties

What Is Paired Data?

How Are Extrapolation and Interpolation Different?

Robustness: The Strength of Statistical Models

The NORM.INV Function in Excel

This Is When the Standard Deviation Is Equal to Zero

What Is Qualitative Data?

The Differences Between Explanatory and Response Variables

The LIPET Strategy for Integration by Parts in Calculus

What Is the Difference Between a Parameter and a Statistic?

A Introduction to Sociology Statistics

Charts, Graphs, Maps Make Your Data Pop

What Is a Population in Statistics?

Moment Generating Functions of Random Variables

How to Use RAND and RANDBETWEEN Functions in Excel

Normal Distribution and Why It Matters

Do You Know How to Use 'If and Only If' in Math Formulas?

Perform Calculations With Norm.Dist and Norm.S.Dist in Excel

Linear Regression and Multiple Linear Regression Analysis

What Are Lambda and Gamma Levels of Association?

What Bimodal Means in Statistics

How to Find ChiSquare Statistical Functions in Excel

What Level and Scale of Measurement Should You Use in Research?

Do You Know the True Value of Pi?

Index of Qualitative Variation Measures Distribution of Variables

How Does Quantitative Data Correlate to the Study of Statistics?

Correlation Analysis: Comparing Variables

What Are De Morgan's Laws?

Inflection Points for the Normal Distribution

Learn How to Use the Term "Data"

Learn More About the Negative Binomial Distribution

Why Is It Useful to Use an Analysis of Variance Test?

Unbiased and Biased Estimators

What Are the Converse, Contrapositive, and Inverse?

How to Use the Z.TEST Function in Excel

Functions with the TDistribution in Excel

Moment Generating Function Can Be an Alternate Way to Solve Problems

Maximum and Inflection Points of the Chi Square Distribution

Find out What the Skewness of an Exponential Distribution Is

Find out How to Use the BINOM.DIST Function in Excel

How to Prove De Morgan's Laws

What Is a Real Number?

What Is a Converse Error?

What Is a Scatterplot and How Is It Used in Statistics?

What Are Confidence Intervals and Confidence Levels in Sociology?

How to Use the STDEV.S Function in Excel

All You Need to Know About the Cauchy Distribution

All about the KURT Function for Kurtosis in Excel

What Is Ecological Correlation?

What's the Difference Between Variance and Standard Deviation?

What Is the Power Set

Calculate Probabilities with A Standard Normal Distribution Table

What Is Statistical Sampling?

How to Calculate a Sample Standard Deviation

Differences Between Population and Sample Standard Deviations

Facts About the Number e: 2.7182818284590452...

Here's How Probability and Statistics Differ

Statistical Correlation, Causation, and Lurking Variables

What Are the Levels of Measurement in Statistics?

Here's a Helpful Example of a ChiSquare Goodness of Fit Test

Compare Two Population Proportions with This Hypothesis Test

What Is a Bell Curve?

What Is Simpson's Paradox in Statistics?

ChiSquare Goodness of Fit Test

Systematic vs. Simple Random Samplings: What's the Difference

All About Histogram Classes

What Is a Histogram and How Is This Graph Used in Statistics?

Examples of Zscore Calculations

Types of Samples in Statistics

Here Your Beginner's Guide to Statistics

Use This Table of Random Digits to Form a Random Sample

How to Make and Use a Stem and Leaf Plot

Inner and Outer Fences to Find Outliers

How Convenience Samples Are Used in Statistics

Example of Two Sample T Test and Confidence Interval

What Is a Relative Frequency Histogram?

The Difference Between Tallies and Counts in Statistics

What Role Does Correlation Play in Statistics?

Bar Graphs Can Show Data Vertically or Horizontally

How Do You Find the Median in Statistics?

An Introduction to Hypothesis Testing

Do You Know What Pie Charts Are, and How to Best Use Them?

A Very Special Bell Curve: Standard Normal Distribution

What Is a Systematic Sample?

Here's How to Make a Boxplot

Calculating Probability With Hypothesis Test Example

How to Conduct a Hypothesis Test

What Is a PValue

How to Use a Table of Random Digits

Can You Calculate These ZScores?

Practice Using Chebyshev's Inequality

A Look at Some Solutions for Challenging Counting Problems

What Is the Probability of the Union of 3 or More Sets?

What Is the Margin of Error Formula for a Population Mean?

A Handy Stats Shortcut for the Sum of Squares

How to Calculate the Variance of a Poisson Distribution

How to Calculate Standard Normal Distribution

How to Calculate the Median of Exponential Distribution

How Many Elements Make a Power Set?

The Center of a Probability Distribution in Expected Value

The Most Commonly Encountered Uncountable Sets

Learn About the ChiSquare Statistic Formula and How to Use It

Practice Problems for ZScores

Do You Know How to Use a Normal Distribution Table for Calculations?

Levels of Measurement Worksheet With Solutions

Learn How to Derive the Formula for Combinations

What Formula Generates the Bell Curve in Statistics?

Probability t Distribution Formula Used in Statistics

Binomial Table for n =10 and n= 11

Courses to Take for a Degree in Statistics

Binomial Table for n=7, n=8 and n=9

Explaining the Binomial Table for n = 2, 3, 4, 5 and 6

Addition Rules in Probability and Statistics

Sample Calculations With the Gamma Function

Worksheet on Combinations and Permuations

The ZScore Formula for Standard Bell Curves

What Is a Student t Distribution Table and When Is It Used?

Expected Value of a Binomial Distribution

What Is a Probability Distribution?

What Is the Definition of a Sample Space in Statistics?

Do You Know the Probabilities for Rolling Two Dice?

What Is the Multiplication Rule for Independent Events?

The Features of a Standard Deck of Cards

How to Calculate the Expected Value

What Are Probability Axioms?

What's the Probability of Going to Jail in Monopoly?

Know When to Use a Binomial Distribution

This Is the Difference of Two Sets in Set Theory

Why Does Zero Factorial Equal One?

The Probability of Rolling a Yahtzee

Chebyshev's Inequality in Probability

What's the Probability of a Full House in Yahtzee in a Single Roll?

How to Find Conditional Probability

The Fundamental Cioncept of Set Theory

How to Use Conditional Probability to Calculate Intersections

What Are the Probability Outcomes for Rolling Three Dice?

How to Use the Normal Approximation for a Binomial Distribution

Here's How Odds Are Related to Probability

Learn How to Calculate Probabilities in Genetics with Punnett Squares

What Is the Factorial (!) in Mathematics and Statistics?

What Is So Important About the Central Limit Theorem?

The Meaning of Mutually Exclusive

What Are the Odds of Having a Flush?

What Is Symmetric Difference in Math?

What Is the Normal Approximation to the Binomial Distribution?

Here's How Combinations and Permutations Differ

How to Use Uniform Distribution to Create a Simple Density Curve

What Is Uniform Probability?

Why Markov's Inequality Is a Helpful Result in Probability

How to Succeed in Statistics Class

What Is the Probability of Randomly Selecting a Prime Number?

Probabilities for Dihybrid Crosses in Genetics

How Probability Plays Into the Game of Monopoly

Find Out How to Prove the Complement Rule in Probability

How to Calculate Expected Value in Roulette

What Is the Empty Set in Set Theory?

What Is the FDistribution?

Probabilities for Liar's Dice

Difference Between Sampling With or Without Replacement

Set Theory: What Is the Intersection of Two Sets?

Find out What the Gamma Function Is

What Is a SigmaField?

What's the Probability of a Large Straight in Yahtzee in One Roll?

The Complement Rule in Statistics: Probability Example

Learn to Calculate Probabilities with Tree Diagrams

See Why You Probably Just Inhaled a Part of Lincoln's Last Breath

See How to Calculate Backgammon Probabilities

What Is a Union in Mathematics?

How to Calculate the Probability of a Small Straight in Yahtzee

Expected Value for ChuckaLuck

What Is a Percentile?

How to Calculate the Correlation Coefficient

How to Estimate the Standard Deviation With the Range Rule

What Does Skewness Mean in Statistics?

What Are the Maximum and Minimum of a Data Set?

What Is the Range of Statistics and When Is It Used?

How to Classify Kurtosis in Statistics

The Slope of the Regression Line and the Correlation Coefficient

Detect the Presence of Outliers With the Interquartile Range Rule

What Are Moments in Statistics?

What Is a TwoWay Table of Categorical Variables?

What Is the Midhinge?

Descriptive vs. Inferential Statistics: What's the Difference?

Understanding the Empirical Rule for Mean, Median, and Mode

How to Use a Time Series Graph

How Do We Determine Outliers in Statistics?

What Are Frequencies and Relative Frequencies?

7 Steps to Creating a Histogram

The Importance of the First and Third Quartiles in Statistics

Understanding the Interquartile Range in Statistics

What Is the Least Squares Line?

Is Mean Absolute Deviation the Same as Standard Deviation?

What Are Residuals?

What Is the 5 Number Summary in Statistics?

Understanding the Uses of Quantiles

Understanding Variance and Standard Deviation

Using Plus Four Confidence Intervals to Estimate Population Proportion

Differences Between The Null and Alternative Hypothesis

How to Construct a Confidence Interval for a Population Proportion

The Difference Between Type I and Type II Errors in Statistics

How to Find Degrees of Freedom in Statistics

Examples of Maximum Likelihood Estimation

Examples of Confidence Intervals for Population Means

Follow This Example of a Hypothesis Test

Stop Making These 4 Mistakes With Your Confidence Intervals

Do You Know How to Calculate the Margin of Error?

What Does It Mean to 'Fail to Reject' a Hypothesis?

What Is a Sampling Distribution?

Parametric and Nonparametric Methods in Statistics

What is an ANOVA Calculation?

Degrees of Freedom in Statistics and Mathematics

What is the Runs Test for Random Sequences?

It's Important to Know the Difference Between Alpha and PValues

Learn What Level of Alpha Determines Statistical Significance

Critical Values with a ChiSquare Table

What Is ANOVA and When Is It Used?

How Confidence Intervals Are Used to Calculate Different Parameters

Which is Worse: Type I or Type II Errors in Statistics?

What Sample Size Do You Need for a Certain Margin of Error?

How to Calculate Confidence Interval for a Mean When You Know Sigma?

See an Example of a Confidence Interval for a Variance

Example ChiSquare Test for a Multinomial Experiment

Degrees of Freedom for Independence in TwoWay Table

Confidence Intervals for the Difference of Two Population Proportions

What is a Permutation Test?

Calculating a Confidence Interval With an Unknown Standard Deviation

How Big Are Millions, Billions, and Trillions?

What Is the Bootstrapping Technique in Statistics?

Queuing Theory: The Mathematical Study of Waiting in Line

Interesting Leap Day Statistics

What Is the St. Petersburg Paradox?

What Are the Odds That You'll Be Dealt a Royal Flush in Poker?

Rescale Test Scores by Using Sten Scores

What Is a Double Blind Experiment?

Example of Bootstrapping in Statistics

How Often Does the Groundhog See His Shadow?

Example Problem for How to Get Stanine Scores

Learn How the Statistics of Political Polls Are Interpreted

Statistics Related to Father's Day