SAT Math
Two-Variable Data
Two-Variable Data is a skill in the Problem-Solving and Data Analysis domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
9 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
The equation y = 2.5x + 40 models the predicted height, y, in millimeters, of a seedling x weeks after it was planted. Based on this model, what is the predicted height of the seedling 10 weeks after it was planted?
- A. 25
- B. 425
- C. 65 ✓
- D. 52.5
Correct answer: C. Substituting x = 10 gives y = 2.5(10) + 40 = 25 + 40 = 65 millimeters.
A scatterplot of a city's monthly ice cream sales versus its monthly average temperature has a correlation coefficient of r = 0.87. Which of the following best describes the relationship shown?
- A. No meaningful linear association
- B. A strong negative linear association
- C. A weak positive linear association
- D. A strong positive linear association ✓
Correct answer: D. A correlation coefficient close to 1, such as 0.87, indicates a strong positive linear association between the two variables.
A researcher modeled a data set with the line y = 2.5x + 40. The table shows four data points from the set: (4, 55), (8, 58), (12, 66), and (16, 90). Which of these points has the largest residual in absolute value — that is, whose actual y-value differs most from the value predicted by the line?
- A. (16, 90) ✓
- B. (8, 58)
- C. (12, 66)
- D. (4, 55)
Correct answer: A. The line predicts y = 2.5(16) + 40 = 80 at x = 16, so the residual is 90 − 80 = 10, the largest in absolute value among the four points (compared to residuals of 5, −4, and −2 at the other points).
A scientist records the population of a bacteria colony at equal time intervals: 5, 10, 20, 40, and 80, in thousands. Which type of function best models this relationship between time and population?
- A. an exponential function, since the population approximately doubles during each equal time interval ✓
- B. a linear function, since the population increases by a positive amount during each time interval
- C. a quadratic function, since the population increases at a faster rate over time
- D. a linear function, since the differences between consecutive values are all positive
Correct answer: A. Correct — a constant ratio between consecutive values, here each term is about twice the one before it, is the defining feature of exponential growth, not linear growth, which would instead require a constant difference between terms.
A pond's water temperature, in degrees Fahrenheit, was recorded every two hours: 70 at hour 0, 68 at hour 2, 60 at hour 4, 55 at hour 6, and 53 at hour 8. During which two-hour interval did the temperature decrease at the greatest average rate?
- A. hour 0 to hour 2
- B. hour 2 to hour 4 ✓
- C. hour 4 to hour 6
- D. hour 6 to hour 8
Correct answer: B. Correct — the average rate of change from hour 2 to hour 4 is (60 minus 68) divided by (4 minus 2), or negative 4 degrees per hour, a steeper decrease than any other two-hour interval in the data.