A plain text format prints the formula out as a single line, which is easier to type if you’re limited

to the characters on a keyboard:

You must know how to read both types of formula displays — typeset and plain text. The

examples in this chapter show both styles. But you may never have to construct a professional-

looking typeset formula (unless you’re writing a book, like we’re doing right now). On the other

hand, you’ll almost certainly have to write out plain text formulas as part of organizing,

preparing, editing, and analyzing your data.

Checking out the building blocks of formulas

No matter how they’re written, formulas are essentially recipes that tell you how to calculate a result,

or how a value is defined. To cook up your own result, you need to know how to follow the recipe.

When initially approaching a formula, it’s helpful to start by examining the building blocks from which

formulas are constructed. These include constants, which are numbers with specified values, and

variables, which represent quantities that can take on different values at different times.

Constants

Constants are values that can be represented explicitly (using the numerals 0 through 9 with or without

a decimal point), or symbolically (using a letter in the Greek or Roman alphabet). Symbolic constants

represent a particular value important in mathematics, physics, or some other discipline, such as:

The Greek letter π usually represents 3.14159 (plus a zillion more digits). This Greek letter is

spelled pi and pronounced pie, and represents the ratio of the circumference of any circle to its

diameter.

The number 2.71828 (plus a zillion more digits) is represented by e (which is italicized when

written, and is pronounced like the letter “e”). Later in this chapter, we describe one way e is used.

You’ll see e in statistical formulas throughout this book and in almost every other mathematical and

statistical textbook. Whenever you see an italicized e in this book, it refers to the number 2.718

unless we explicitly say otherwise.

The official mathematical definition of e is: The value of the expression

, which

approaches infinity as n gets larger and larger. Unlike π, e has no simple geometrical

interpretation. Here is an example used to help learners envision e: Assume you put exactly one

dollar in a bank account that’s paying 100 percent annual interest, compounded continuously. After

exactly one year, your account will have e dollars in it. That includes the interest on your original

dollar, plus the interest on the interest — about $1.72 (to the nearest penny) — added to the

original dollar for a total of $2.72. (This is just an example. We don’t think there is a single bank

out there advertising annual returns in terms of e!)