you write down all the whole numbers from 1 to the factorial number in a row, and then multiply them

all together. For example, the expression 5!, which is read as five factorial, means to calculate

(which equals 120).

Even though standard keyboards have a ! key, most computer programs and spreadsheets don’t let you

use ! to indicate factorials. For example, to do the calculation of 5! in Microsoft Excel, you use the

formula =FACT(5).

Here are a few factorials fun facts:

Factorials can be very large. For example, 10! is 3,628,800, and 170! is about

, which

is close to the processing limits for many computers.

0! isn’t 0, but is actually 1. Actually, it’s the same as 1!, which is also 1. That may not make

obvious sense, but is true, so you can memorize it.

The definition of factorial can be extended to fractions and even to negative numbers. But good

news! You don’t have to deal with those kinds of factorials in this book.

Absolute values

The term absolute value refers to the value of a number when it is positive (meaning it has no minus

sign before it). You indicate absolute value by placing vertical bars immediately to the left and right of

the number. So |5.7| equals 5.7, and |–5.7| also equals 5.7. Even though most keyboards have the |

(pipe) symbol, the absolute value is usually indicated in plain text formulas as abs(5.7).

Functions

In this book, a function is a set of calculations that accepts one or more numeric values (called

arguments) and produces a numeric result. Regardless of typeset or plain text, a function is indicated

in a formula by the function name followed by a set of parentheses that contain the argument or

arguments. Here’s an example of the function square root of x: sqrt(x).

The most commonly used functions have been given standard names. The preceding sections in this

chapter covered some of these, including sqrt for square root, exp for exponentiate, log for logarithm,

ln for natural log, fact for factorial, and abs for absolute value.

When writing formulas with functions using software, be aware that each software may have

rules about case-sensitivity. It may require all caps, all lowercase, or first-letter capitalization.

Make sure to check the software’s documentation for guidance (Chapter 4 discusses different

statistical software packages.)

Simple and complicated formulas

Simple formulas have one or two numbers and only one mathematical operator (for example,

).

But most statistical formulas you’ll encounter are more complicated, with two or more operators and

variables.