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.