SAT: Percentages & Data Interpretation Cheat Sheet
The core ideas of SAT: Percentages & Data Interpretation distilled into a single, scannable reference — perfect for review or quick lookup.
Quick Reference
Percent Change
The ratio of the change in a quantity to the original quantity, expressed as a percentage: $\text{Percent Change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$.
Successive Percent Changes
When multiple percent changes are applied in sequence, each applies to the result of the previous change, not the original value. Multiply the successive factors.
Two-Way Frequency Table
A table that displays counts for two categorical variables simultaneously. Rows represent one variable, columns represent the other, and margins show totals.
Conditional Relative Frequency
A joint count divided by a specific row or column total, answering questions like 'Given that someone is female, what fraction voted yes?'
Markup and Discount
Markup adds a percentage to the cost to set a selling price: $\text{Price} = \text{Cost} \times (1 + r)$. Discount subtracts a percentage: $\text{Sale Price} = \text{Original} \times (1 - r)$.
Joint Frequency
The count in a single interior cell of a two-way table, representing observations that satisfy both the row and column categories.
Marginal Frequency
The total for an entire row or column in a two-way table, found by summing across that row or down that column.
Finding the Original from a Percent
When a value after a percent change is known, divide by the multiplier to find the original: if $x \times (1 + r) = \text{result}$, then $x = \frac{\text{result}}{1 + r}$.
Probability from a Table
The probability of an event from a two-way table is the favorable count divided by the appropriate total (grand total for unconditional, row/column total for conditional).
Relative Frequency
A frequency expressed as a fraction or percentage of a total, converting raw counts into comparable proportions.
Key Terms at a Glance
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