Math: Data & Problem Solving·Data Interpretation

SAT Math — Data Interpretation: Tables, Graphs, and Scatterplots

What Data Interpretation Questions Look Like

These questions give you a graph, table, or chart and ask you to:

  • Read a specific value from the data
  • Calculate a percentage or ratio
  • Identify a trend or pattern
  • Compare two quantities
  • Evaluate whether a conclusion is supported by the data

    • The most common formats: bar charts, line graphs, two-way tables, and scatterplots.

    Two-Way Tables

    A two-way table shows frequencies for two categorical variables.

    Example: | | Prefers Coffee | Prefers Tea | Total | |---|---|---|---| | Male | 45 | 25 | 70 | | Female | 30 | 40 | 70 | | Total | 75 | 65 | 140 |

    Reading the table:

  • 45 males prefer coffee
  • 65 total people prefer tea
  • 75/140 ≈ 53.6% of all respondents prefer coffee

    • Conditional probability from tables: "What fraction of females prefer coffee?" = 30/70 ≈ 42.9% (You're looking at females ONLY — use the female row total, not the grand total)

    Scatterplots

    A scatterplot shows the relationship between two numerical variables. Each point represents one data observation.

    What to look for:

  • Direction: Positive correlation (both rise together) or negative correlation (one rises as the other falls)
  • Strength: Points tightly clustered around a line = strong correlation; scattered widely = weak
  • Outliers: Points that don't fit the overall pattern

    • Line of best fit (trend line): The SAT often shows a line drawn through the data and asks you to:

  • Estimate the value for a given x using the line
  • Identify the slope of the line
  • Recognize which data point is an outlier (far from the line)

    • Correlation vs. causation: Scatterplots show correlation — not causation. Even if ice cream sales and drowning rates rise together (both increase in summer), that doesn't mean ice cream causes drowning.

    Percentages and Ratios from Data

    The SAT tests your ability to extract percentages and ratios from graphs.

    Key formula: Percent = (Part/Whole) × 100

    Watch out for:

  • "What percent of X are Y?" → Use only the X row/column as the denominator
  • "What percent of the TOTAL are Y?" → Use the grand total as the denominator

    • Real-world example: A bar chart shows that a school has 240 students: 100 freshmen, 70 sophomores, 40 juniors, and 30 seniors. A question asks: "What percent of students are freshmen?" Answer: 100/240 × 100 = 41.7%.

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    Key Terms

  • Two-way table: A frequency table with two categorical variables
  • Conditional probability: Probability given a specific condition (use the condition's row/column total as denominator)
  • Scatterplot: Graph showing the relationship between two numerical variables; each point is one data observation
  • Line of best fit: A line drawn through scatterplot data that minimizes the overall distance from the data points to the line
  • Positive correlation: Both variables increase together
  • Negative correlation: One variable increases as the other decreases
  • Outlier: A point that doesn't fit the general pattern of the scatterplot
  • Correlation vs. causation: Two things moving together doesn't prove one causes the other

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Quiz Questions:

Use this table for Q1 and Q2: | | Passed | Failed | Total | |---|---|---|---| | Studied | 60 | 10 | 70 | | Did not study | 15 | 35 | 50 | | Total | 75 | 45 | 120 |

Q1. What percent of all students passed?

A) 60% B) 62.5% C) 75% D) 80%

Answer: B — 75 students passed out of 120 total: 75/120 × 100 = 62.5%.

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Q2. What fraction of students who did NOT study still passed?

A) 15/120 B) 15/50 C) 15/75 D) 35/50

Answer: B — The question asks about students who DID NOT study — use that row's total (50) as the denominator. 15 of those students passed. 15/50 = 30%.

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Q3. A scatterplot shows a strong negative correlation between hours of TV watched per day and GPA. A student concludes: "Watching TV causes lower GPAs." This conclusion:

A) Is fully supported by the scatterplot B) Is not supported — the scatterplot shows correlation, not causation; other factors may explain both variables C) Is partially supported if the correlation coefficient is above 0.5 D) Is supported only if more than 100 data points are shown

Answer: B — Correlation does not establish causation. There could be a third variable (e.g., students who struggle academically may also have more free time to watch TV). The scatterplot cannot prove that TV watching causes lower GPAs.

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Q4. A line of best fit on a scatterplot has the equation y = 2x + 5. What does the slope (2) tell you?

A) The starting value of y when x = 0 is 2 B) For each 1-unit increase in x, y is predicted to increase by 2 units C) There are exactly 2 data points for every x value D) The correlation between x and y is 2

Answer: B — The slope of a line of best fit represents the rate of change — for each 1-unit increase in x, the predicted value of y increases by 2. Choice A describes the y-intercept (5, not 2). Correlation is a number between −1 and 1, not a slope.

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Q5. A bar chart shows annual sales (in millions) for four product lines. Product A: $12M, Product B: $18M, Product C: $8M, Product D: $22M. What percent of total sales does Product D account for?

A) 22% B) 36.7% C) 50% D) 28.5%

Answer: B — Total = 12 + 18 + 8 + 22 = $60M. Product D: 22/60 × 100 = 36.7%.