Math

Mastering the Formal Geometry Proof

Suppose you need to solve a crime mystery. You survey the crime scene, gather the facts, and write them down in your memo pad. To solve the crime, you take the known facts and, step by step, show who committed [more…]

Sizing Up the Area of a Polygon

Not only can polygons be classified by the number of sides they have and by their angles, but they can also be grouped according to some of their qualities. Polygons can have three personality characteristics [more…]

Simple and Easy Geometry Tips and Tools

The first rule of life? Life (as well as geometry) can be difficult. But why make it more difficult than it has to be? Do you need help with geometry? Here are 11 tried-and-true tips to make your forays [more…]

Measuring and Making Angles

On a map, you trace your route and come to a fork in the road. Two diverging roads split from a common point and form an angle. The point at which the roads diverge is the [more…]

Classifying Three Types of Triangles

Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves. That is, a triangle has [more…]

Summarizing Categorical Data in Statistics

Categorical data capture qualities or characteristics about the individual, such as a person's eye color, gender, political party, or opinion on some issue [more…]

How SPSS (Statistical Package for the Social Sciences) Works

The developers of the Statistical Package for the Social Sciences (SPSS) made every effort to make the software easy to use. This prevents you from making mistakes or even forgetting something. That's [more…]

Raising the Bar on Bar Graphs in Statistics

A bar graph, or bar chart, is perhaps the most common data display used by the media. Like a pie chart, a bar graph breaks categorical data down by group, showing how many are in each group. A bar graph [more…]

Statistics: More than Just Numbers

Most statisticians don't want statistics to be thought of as "just statistics." While the rest of the world views them as such, statisticians don't think of themselves as number crunchers; more often, [more…]

Defining the Radian in Trigonometry

A person's introduction to angles is usually in terms of degrees. You probably have a good idea of what a 45-degree angle looks like. And even most middle-school students know that a triangle consists [more…]

Discovering Pythagorean Triples

The Pythagorean Theorem is certainly one of the most famous theorems in all of mathematics. Mathematicians and lay people alike have studied it for centuries, and people have proved it in many different [more…]

Mathematical Matryoshka: Counting Numbers, Integers, Rational Numbers, and Real Numbers

When you first start dealing with numbers, you learn about the four main sets, or groups, of numbers, which, like Russian matryoshka dolls, nest inside one another: [more…]

Figuring Out What Probability Means

Probabilities come in many different disguises. Some of the terms people use for probability are chance, likelihood, odds, percentage, and proportion. But the basic definition of [more…]

Multiplying with Scientific Notation

Multiplying numbers that are in scientific notation is fairly simple because multiplying powers of 10 is so easy. Here's how to multiply two numbers that are in scientific notation: [more…]

The Four Ways to Talk to SPSS

More than one way exists for you to command the Statistical Package for the Social Sciences (SPSS) to do your bidding. And you don't have to choose one and stick with it — you can perform tasks using whichever [more…]

Using Probability When Hitting the Slot Machines

Remember the movie National Lampoon's Vegas Vacation, when gambling fever consumes Chevy Chase's character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty [more…]

Generalizing Statistical Results to the Entire Population

Making conclusions about a much broader population than your sample actually represents is one of the biggest no-no's in statistics. This kind of problem is called [more…]

Crunching Numbers: Writing in Scientific Notation

Scientific notation is a system for writing very large and very small numbers that makes them easier to work with. Every number can be written in scientific notation as the product of two numbers: [more…]

Building Logical Arguments

When people say "Let's be logical" about a given situation or problem, they usually mean "Let's follow these steps:"

1. Figure out what we know to be true. [more…]

Statistics Conundrums: Dealing with Survey Nonresponders

Nonresponders are always a problem when you're calculating the results of a survey. Before you can crunch the numbers in all the surveys you get back, you have to decide what to do about the surveys you [more…]

Recognizing the Impact of Statistics in Polls

A survey is an instrument that collects data through questions and answers and is used to gather information about the opinions, behaviors, demographics, lifestyles, and other reportable characteristics [more…]

How to Use the Order of Operations

Follow the order of operations with each algebra problem you solve. The order of operations in algebra is important if you want to find the correct answer. You first work through any grouping symbols, [more…]

Cramer’s Rule for Linear Algebra

Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]

Algebraic Permutations and Combinations

In algebra, you use permutations to count the number of subsets of a larger set. Use permutations when order is necessary. With combinations, you can count the number of subsets when order doesn't matter [more…]