Introduction to Statistics, Percentages, and Numerical Properties

Struggling through difficult material strengthens memory retention and deepens long-term understanding.
Chapter 1 contains foundational background knowledge for applying statistics, as well as specific material assessed in midterm exams.

The percentage symbol ( $\%$ ) represents a concrete value equal to $\frac{1}{100}$ or $0.01$ .
Percentages are unitless ratios expressing a proportion out of $100$ , rather than absolute counts.
To convert a percentage to a decimal, divide by $100$ by shifting the decimal point two places to the left (e.g., $96\% = 0.96$ ).
To convert a decimal to a percentage, multiply by $100$ by shifting the decimal point two places to the right (e.g., $0.56 = 56\%$ ).
In word problems, the word "of" denotes multiplication (e.g., $6\%$ of $1200$ \text{ responses} translates to $\frac{6}{100} \times 1200 = 72\,\text{responses}$ ).

Every number in statistics possesses an explicit or implicit decimal point.
Leading zeros prior to significant digits serve as essential placeholders and must be retained.
Statistical values generally carry units, with the exception of relative measurements like ratios, percentages, and probabilities.
Statistical analysis primarily focuses on positive real numbers starting from zero ( $0$ ).
Probability is expressed as a unitless numerical value bounded between $0$ and $1$ .

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