Key Concepts Study Tool: Chapter 02

1. Order of Operations: BEDMAS

2. Fractions and Decimals

Fractions and decimals are different ways of expressing non-integers. Integers are round numbers such as –2, –1, 0, 1, 2, etc.
Examples of non-integers include –1.5, 0.5,1.5, etc.
Fractions and decimals are really just different ways of stating the same thing. For example, the fraction 1/2 is equal to 0.50.

3. Exponents (“raising to a power”)

Form: X^m, where m (the exponent) stands for how many times X is being multiplied by itself.
X= the base; m = the power
E.g., X * X * X * X * X = X⁵
X^a * X^b= X^a+b BUT X^a * Y^b ≠ XY^a+b.
Inverse function is the root (E.g., 2²=4 then √4=2)

4. Logarithms

log_baseProduct = Power e.g., log₁₀1000 = 3
When base = 10 it is a common logarithm
When base= 2.718 it is a natural logarithm (also called base e) (what we use in the text)

5. Levels of Measurement

Nominal: Response only name things, they cannot be ranked, and distance between response categories cannot be measured (e.g., gender, religious affiliation).
Ordinal: Responses can be ranked, but the distance between response categories cannot be measured (e.g., Likert surveys: 1 = extremely dissatisfied … 5 = extremely satisfied).
Interval: Responses can be put into an order and ranked, and the distance between categories can be measured, but there is no theoretical zero. Responses can be added or subtracted but not multiplied or divided (e.g., temperature in Fahrenheit).
Ratio: Responses can be ranked, the distance between observations can be measured(can multiply, divide, add or subtract), and there is a theoretical zero, meaning a score of zero means an absence of whatever you are measuring (e.g., age, income).