Basic Mathematical Operations for Use in Statistics

By John Pezzullo

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

Multiplication is indicated in several ways.

Multiplication Options
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
multiplied together
Raised dot 2 · 5 = 10 Typeset formula
Something immediately in front of a parenthesized
expression
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 r (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.

Division

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:

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