Basic Mathematical Operations for Use in Statistics
The four basic mathematical operations are addition, subtraction, multiplication, and division (ah, yes — the basics you learned in elementary school). Different symbols indicate these operations.
Addition and subtraction
Addition and subtraction are always indicated by the + and – symbols, respectively, placed between two numbers or variables. The minus sign has some other tricks up its sleeve, though:
A minus sign immediately in front of a number means a negative quantity. For example, –5 could indicate five degrees below 0 or a weight loss of 5 kilograms.
A minus sign in front of a variable tells you to reverse the sign of the value of the variable. Therefore, –x means that if x is positive, you should now make it negative; but if x is negative, make it positive. Used this way, the minus sign is referred to as a unary operator, because it’s acting on only one variable.
Multiplication is indicated in several ways.
|What It Is||Example||Where It’s Used|
|Asterisk||2 * 5 = 10||Plain text formulas, but almost never in typeset formulas|
|Cross||2 × 5 = 10||Typeset formula, between two variables or two constants being
|Raised dot||2 · 5 = 10||Typeset formula|
|Something immediately in front of a parenthesized
|2(5 + 3) = 16||Typeset formula|
|Brackets and curly braces||2[6 + (5 + 3)/2] = 20||Typeset formula containing “nested” parentheses|
|Two or more terms running together||2πr (versus 2 x π x r)||In typeset formulas only.|
You can’t run terms together to imply multiplication just anytime. For example, you can’t replace 5 x 3 with 53 because 53 is an actual number itself. And you shouldn’t replace length x width with lengthwidth because people may think you’re referring to a single variable named lengthwidth.
You may run terms together to imply multiplication only when it’s perfectly clear from the context of the formula that the authors are using only single-letter variable names and that they’re describing calculations where it makes sense to multiply those variables together, such as Area of a rectangle = hw, where h= height and w = width.
Like multiplication, division is indicated in several ways:
A slash (/) in plain text formulas: Rate = Distance / Time
A division symbol in typeset formulas: Rate = Distance ÷ Time
A long horizontal bar in typeset formulas: