The trichotomy property in mathematics is important because of what is says about ordering of the real numbers.

What Is a One-tailed Test?

One-tailed tests of significance occur throughout statistics when our alternative hypothesis contains an inequality.

Formulas for Combinations and Permutations

Combinations and permutations are ways to count collections of objects.

Formulas for Combinations and Permutations

Combinations and permutations are ways to count collections of objects. Page 2.

Permuatation Formula

Combinations and permutations are ways to count collections of objects.

What Is a Uniform Distribution

A uniform distribution is one of the simplest types of probability distributions. This type of distribution arises when every outcome in the sample space has the same probability.

Notable Statisticians

Notable Statisticians, famous statisticians

Pascal, Fermat and the Birth of Probability

Learn more about the beginnings of probability when Pascal and Fermat teamed up to solve a problem involving dice.

Use of the Moment Generating Function for the Binomial Distribution

See how to use the moment generating function to calculate the mean and variance of a binomial distribution.

What Are Maclaurin Series?

Maclaurin Series use the derivatives of a function as coefficients in a power series. They can be used for a number of applications.

Luca Pacioli and the Beginnings of Probability

One of the origins of probability stems from when Luca Pacioli posed a mathematical question regarding a game of chance.

What is a Moment Generating Function?

The moment generating function of a random variable is related to a particular expected value.

What Is the Geometric Series Test?

There is an easy test to determine if a geometric series converges. We also see a formula for determining the value of a convergent geometric series.

Careers

Careers in statistics, statistics jobs, jobs in statistics

Lesson Plans

Lesson plans for statistics, statistics class ideas

Practice Problems

Statistics Practice, Statistics Problems, Statistics Worksheets

What Is a Counterexample?

Counterexamples are specific types of examples that are used to disprove mathematical statements.

What Is the Cantor Set?

The Cantor set is a surprising example. While it seems like there should not be many points in the set, there are actually an uncountable number.

What Is the Probability of Rolling a Full House in Yahtzee?

Yahtzee is a dice game in which players roll for different combinations of dice. Find out what the probability is of rolling a full house in a single roll.

Example Chi-Square Test for a Multinomial Experiment

See two examples of how a chi-square test is used in dealing with a multinomial experiment.

The Difference Between Probability and Statistics

Probability and Statistics are two closely related mathematical subjects. What is the difference between probability and statistics?

Uncountably Infinite Sets

Not all infinite sets are the same as some are

Examples of Uncountable Sets

Infinite sets can be classified as countable or uncountable. See some examples of uncountable sets.

The box of the boxplot

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph.

How to Make a Boxplot

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph.

Comparing Data

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph.

Introduction to Boxplots

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph.

Draw Two Whiskers

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph.

How to Make a Boxplot: Begin With a Number Line

Boxplots, or box and whisker plots, assemble the range, median and quartiles of a data set. Two or more sets of data can be compared by looking at the boxes and whiskers of the graph. Page 2.

Binomial Probability Distribution Formula

The binomial distribution formula is used to calculate probabilities.

Worksheet on Averages

Try finding the mean, median, mode and midrange of some data.

Conditional Probability - Notation and Examples

For conditional probability we are calculating the probability of an event, based upon the fact that another event has already occurred.

Probability Puzzles - Odds of a Flush in Poker

A flush is a hand in poker that has five cards of the same suit. Discover how unlikely this is to occur.

What Is the Least Squares Line?

The least squares line is the unique line that passes through the midst of a set of paired data in such a way that the distances from the points to the lines are minimized. Find out how precisely this is done.

What Is the Cartesian Product

The Cartesian product is a construction in set theory that makes a new set out of two other sets. See how this is done and why it is called a product.

What Is a Geometric Series?

Geometric series are related to geometric sequences. Each successive term in the series is related to the preceding term by a common ratio.

What Is the Probability of almost winning the Lottery

It very unlikely to win the lottery. What is the probability of almost winning millions of dollars?

Margin of Error Formula

The margin of error of the mean of a normally distributed population can be calculated in just a few steps with the appropriate formula.

Probability of Rolling a Yahtzee in Yahtzee Jr.

Yahtzee Jr. is a modification of the traditional Yahtzee dice game. Find out what happens when one of the sides of the dice is wild.

How Many Elements Are in the Power Set

The power set is a construction in set theory involving the subsets of a given set. If this set is finite, there is a formula that tells us how many elements are in the power set.

What Is the Power Set

The power set is a construction in set theory that collects together all subsets of a given set.

What Is a Sample Space in Statistics?

A sample space is an important concept in probability. This topic is concerned with all of the possible outcomes of a probability experiment.

The Fundamental Theorem of Calculus Part I

The first part of the fundamental theorem of calculus can be used in mathematical statistics. This theorem is particularly useful to change a cumulative distribution function to a probability density function.

Solutions for Challenging Counting Problems

Counting arrangements of objects can seem like a formidable task, but with a little thought these mathematical problems become more manageable.

Difference Between Extrapolation and Interpolation

Interpolation and extrapolation are similar sounding techniques. Find out the difference between them.

How to Find the Analysis Toolpak in Excel 2010

To conduct some more advanced statistical techniques, it is necessary to add the analysis toolpak to Excel. See step-by-step instructions on how to do this so that you can use Excel for your own data analysis.

Examples of Slope-Intercept Form

One form for the equation of a straight line is the slope-intercept form. See several examples of problems related to the equation of a line.

What Is a Quantile

Quantiles are a generalization of percentiles for a continuous random variable. Learn more about this measurement of position and see how calculus is used.

Slope of a Line

One important measurement associated with a straight line is that of the slope. Learn about this topic and how it is used in statistics.

What Is a Logarithmic Function

Logarithmic functions are a class of functions that are inverse to exponential functions. Learn more about these types of functions.

The Number Pi: 3.14159265...

Learn more about the number pi (3.14159... ) and where this popular number shows up in statistics and probability

What Is Integration by Parts?

There are many methods of integration that it is important to master in mathematical statistics. One of these is called integration by parts.

An Estimate for Pi

This classroom activity alters Buffon's needle throwing experiment to provide an estimate for the number pi.

Example of Goodness of Fit Test

The chi-square goodness of fit test is used to determine if population proportions match a hypothetical model. See an example of how this kind of test can be used.

Chi-Square Goodness of Fit Test

The chi-square goodness of fit test is a way to determine how close a categorical variable aligns with a theoretical model.

Chi-Square in Excel

Excel can be used to do many statistical calculations. Learn more about the CHISQ.DIST, CHISQ.DIST.RT, CHISQ.INV, CHISQ.INV.RT, CHIDIST and CHIINV functions in Excel.

What Is a Stratified Sample

Some populations naturally split into several non-overlapping segments. A stratified sample recognizes this and seeks to contain representatives from all of these segments.

What Is an Exponential Function

Functions are classified into several different types. One of these is called an exponential function.

Examples of Proof by Induction

Mathematical induction is a type of proof strategy. Sometimes when learning about mathematics it is helpful to see examples worked out. Check out a couple of examples of proofs using mathematical induction.

Degrees of Freedom for Independence of Variables in Two-Way Table

One type of hypothesis test concerns the independence of two categorical variables. See how to calculate the number of degrees of freedom for this type of test of significance.

What Is a Confidence Interval

Confidence intervals are a major part of inferential statistics. The basic idea behind this concept is that we use sample data to estimate a population parameter. See how this is accomplished.

What Is a Sampling Distribution?

An important topic in statistics is that of a sampling distribution. By considering a simple random sample as being derived from a distribution of samples of equal size, we can use results from probability and mathematical statistics to reduce variability.

What Is the Conservative Approximation?

For inference with two independent populations the number of degrees of freedom can be determined with Welch's formula. A conservative approximation involves much less calculation.

What Is a P-Value

P-Values are used in hypothesis tests and indicate the degree of evidence that we have against the null hypothesis.

Examples of Confidence intervals for means

See worked out examples of problems involving confidence intervals about the mean

When Do You Use a Multinomial Experiment

See out what conditions are necessary in order to use a multinomial experiment.

Levels of Measurement Worksheet

Practice identifying levels of measurement with this worksheet.