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Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
15
Percentages and data interpretation questions account for a significant portion of the SAT Math section, appearing in both the Problem-Solving and Data Analysis domain and the Heart of Algebra domain. These questions test your ability to calculate percent change, work backwards from discounted or marked-up prices, interpret two-way frequency tables, and extract meaning from data presentations. The SAT rewards students who can translate between fractions, decimals, and percents fluently and who can identify which value serves as the base (denominator) in a percent calculation.
Two-way frequency tables are a hallmark of SAT data questions. You may be asked to find joint frequencies, marginal totals, conditional relative frequencies, or probabilities from tables that categorize data by two variables. Understanding the difference between row totals and column totals, and knowing when to use the grand total versus a subtotal as your denominator, is critical for avoiding the most common mistakes on these questions.
Beyond tables, the SAT tests successive percent changes (a 20% discount followed by a 10% discount is not 30% off), percent of a percent, and real-world contexts like tax, tip, markup, and commission. Data interpretation questions may also involve reading bar charts, histograms, or circle graphs and connecting visual information to percent calculations. Mastering these skills builds a foundation for statistics and prepares you for the kinds of quantitative reasoning demanded in college coursework and professional settings.
One step at a time.
The ratio of the change in a quantity to the original quantity, expressed as a percentage: $\text{Percent Change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$.
Example: A price rises from $\$50$ to $\$60$. Percent increase = $\frac{60 - 50}{50} \times 100\% = 20\%$.
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.
Example: A $\$120$ item is 30% off, then an extra 10% off the sale price: $120 \times 0.70 \times 0.90 = \$75.60$ (not 40% off).
A table that displays counts for two categorical variables simultaneously. Rows represent one variable, columns represent the other, and margins show totals.
Example: A table with rows Male/Female and columns Yes/No shows how many males said yes, females said no, etc.
A joint count divided by a specific row or column total, answering questions like 'Given that someone is female, what fraction voted yes?'
Example: If 21 of 35 women voted yes, the conditional relative frequency of yes given female is $\frac{21}{35} = 0.60$.
Markup adds a percentage to the cost to set a selling price: $\text{Price} = \text{Cost} \times (1 + r)$. Discount subtracts a percentage: $\text{Sale Price} = \text{Original} \times (1 - r)$.
Example: A store marks up a $\$40$ item by 25%: $40 \times 1.25 = \$50$. A 15% discount on $\$80$: $80 \times 0.85 = \$68$.
The count in a single interior cell of a two-way table, representing observations that satisfy both the row and column categories.
Example: In a survey table, the cell at row 'Seniors' and column 'Prefer online' shows the count of seniors who prefer online learning.
The total for an entire row or column in a two-way table, found by summing across that row or down that column.
Example: If a 'Yes' column has entries 10 and 21, the marginal frequency for 'Yes' is $10 + 21 = 31$.
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 $x = \frac{\text{result}}{1 + r}$.
Example: After a 20% discount, a shirt costs $\$32$. Original = $\frac{32}{0.80} = \$40$.
More terms are available in the glossary.
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