Problem-Solving and Data Analysis

Ratios, Rates, Proportions: forms

a:b \frac{a}{b}

Ratios, Rates, Proportions: how to solve porportions

cross multuply \frac{a}{d}=\frac{b}{c}

Ratios, Rates, Proportions: Unit conversion

Multiply when bigger divide when smaller

Percentages: Part Formula

\text{Part} = \text{Whole} \times \tfrac{\text{Percentage}}{100}.

Percentages: Whole formula

\text{Whole} = \tfrac{\text{Part}}{\text{Percentage}/100}.

Percentages: Percentage formula

\text{Percentage} = \tfrac{\text{Part}}{\text{Whole}} \times 100.

Percentages: Percent change

\tfrac{\text{New} - \text{Old}}{\text{Old}} \times 100\%.

One-Variable Data: Mean

\displaystyle \bar{x} = \tfrac{1}{n}\sum{i=1}^{n}xi .

One-Variable Data: median

middle value after ordering

One-Variable Data: Mode

most frequent value.

One-Variable Data: Range

\text{max} - \text{min}.

One-Variable Data: Standard Deviation

quantitative spread measure (greater SD = data more spread out).

Two-Variable Data (Scatterplots) : Line of Best Fit

Desmos

Two-Variable Data (Scatterplots): r=1 corr\left(x_1,y_1\right)

perfect positive

Two-Variable Data (Scatterplots) r=-1 corr\left(x_1,y_1\right)

perfect negative

Two-Variable Data (Scatterplots) corr\left(x_1,y_1\right) r=0

no linear relationship

Probability: Basic probability

P(A) = \tfrac{\text{favorable outcomes}}{\text{total outcomes}}.

Probability: Conditional Probability

P(A\mid B) = \tfrac{P(A \text{ and } B)}{P(B)}.

Inference & Statistics: Margin of error for 95\% confidence

\text{MOE} \approx \tfrac{1}{\sqrt{n}}.

Inference & Statistics: Observational study

measure without intervention (shows correlation).

Inference & Statistics: Experimental study

apply treatment (Supports causation)