Statistics, Data Interpretation, and Distributions: SAT Practice Questions & Study Guide
Questions requiring you to calculate and interpret measures of center and spread, read graphs and tables, and understand the shape of data distributions.
Understanding Statistics, Data Interpretation, and Distributions on the SAT
Statistics on the SAT is primarily about interpretation and conceptual reasoning, not computation. You need to know that the mean (arithmetic average) is pulled toward outliers, while the median (middle value when sorted) is resistant to extreme values. The mode is the most frequently occurring value. When a data set is perfectly symmetric, mean = median = mode; when it is skewed right (long tail to the right), the mean > median; when skewed left, the mean < median.
Measures of spread describe how dispersed the data are. Range is simply max − min. Standard deviation measures average distance from the mean—a larger standard deviation means the data are more spread out. You will never calculate standard deviation by hand on the SAT, but you will need to identify which data set has greater or lesser spread by inspecting a graph or table. Interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of data and is robust to outliers.
Data interpretation questions ask you to read values from bar charts, line graphs, scatterplots, histograms, and two-way tables. The most common errors involve misreading scales (e.g., not noticing a y-axis that starts at 50 rather than 0) or misidentifying the correct variable from a legend. For scatterplots, the line of best fit question type asks you to use the equation given (or visually estimate the slope) to predict values or describe the trend.
Distribution shape questions describe data as symmetric, left-skewed, or right-skewed, and ask what this implies about the relative positions of mean, median, and mode. A normal (bell-shaped) distribution is symmetric. In real-world contexts, income distributions are typically right-skewed (mean > median), while distributions of test scores or heights are often approximately normal.
Key Rules & Formulas
Memorize these rules — they come up directly in SAT questions.
Mean = sum of all values / number of values; median = middle value (or average of two middle values)
Data: {3, 5, 7, 9, 11} — mean = 35/5 = 7; median = 7 (middle of 5 values)
Skewed right → mean > median; skewed left → mean < median; symmetric → mean ≈ median
A household income dataset with a few billionaires will be right-skewed, so the mean income will exceed the median
Adding a constant to every value shifts mean and median by that constant but doesn't change range or standard deviation
If every score increases by 5 points, mean increases by 5 but standard deviation stays the same
Outliers increase the range and pull the mean but leave the median nearly unchanged
Adding a score of 200 to {70, 75, 80, 85, 90} changes mean dramatically but barely shifts the median
Line of best fit: use the given equation to predict y for a given x; the slope represents the rate of change per unit of x
If ŷ = 2.5x + 10, then for x = 8, predicted y = 2.5(8) + 10 = 30
Statistics, Data Interpretation, and Distributions Practice Questions
Select an answer and click Check Answer to reveal the full explanation. Questions go from easiest to hardest.
The ages of five students in a study group are 14, 16, 15, 17, and 18. What is the mean age of the students?
Seven test scores are listed in order: 62, 70, 74, 81, 85, 90, 93. What is the median score?
A dataset has values: 5, 8, 8, 10, 12, 14, 14, 14, 20. Which measure of center is greatest?
A class of 20 students has a mean score of 78. After one more student takes the test, the mean drops to 77. What score did the new student receive?
The table below shows the number of hours per week that 50 employees spend in meetings: Hours | Frequency 0–4 | 12 5–9 | 18 10–14 | 13 15–19 | 7 Which interval contains the median number of hours?
A histogram shows test scores for two classes. Class A's scores are approximately normally distributed with a mean of 75 and a standard deviation of 8. Class B's scores are also normally distributed with a mean of 75 and a standard deviation of 12. Which of the following is true?
A scatterplot shows a positive linear relationship between hours studied (x) and test score (y). The line of best fit has equation y = 4x + 55. According to this model, what score would a student who studied for 10 hours be predicted to receive?
A dataset has a mean of 50 and a median of 42. Which of the following best describes the likely shape of the distribution?
A dataset of 10 values has a mean of 20 and a range of 15. If the largest value is increased by 10 and no other values change, which measures are affected?
The five-number summary for a dataset is: minimum = 10, Q1 = 25, median = 40, Q3 = 60, maximum = 80. A new data point of 95 is added. Which of the following measures will definitely change?
Want more Statistics, Data Interpretation, and Distributions practice?
Access 1,000+ additional questions filtered by difficulty and score band in the full 1600.lol question bank — free, no signup needed.
Common Mistakes to Avoid
These are the most frequent errors students make on Statistics, Data Interpretation, and Distributions questions. Knowing them in advance prevents costly point losses.
- !Misidentifying skew direction—students confuse 'skewed right' with 'most data is on the right'
- !Using mean instead of median when the question asks for the measure that best represents a skewed distribution
- !Reading bar chart heights without accounting for a y-axis that doesn't start at zero
- !Confusing standard deviation with range—they both measure spread but very differently
- !Assuming that a larger sample always gives a smaller standard deviation (it doesn't—sample size affects standard error, not standard deviation)
SAT Strategy Tips: Statistics, Data Interpretation, and Distributions
For any graph question, spend 5 seconds reading the axis labels and scale before extracting numbers—scale tricks are common on the Digital SAT
When comparing two distributions described in a table, compute the mean and range mentally or jot them down before answering the comparison question
Skew questions: imagine which direction the 'tail' of the histogram points—the mean follows the tail
For 'which change would most increase/decrease the mean/median' questions, test a specific extreme value mentally rather than reasoning abstractly
Other Problem Solving & Data Analysis Subtopics
Ratios, Rates, and Proportional Relationships
Questions asking you to set up proportional equations, convert units, and scale quantities in real-world contexts.
Percentages and Percent Change
Questions covering percent conversions, percent increase and decrease, and multi-step percentage problems with real-world price or quantity contexts.
Probability and Conditional Probability
Questions asking you to find simple, compound, and conditional probabilities, often from two-way frequency tables.
Statistical Inference and Study Design
Questions testing whether you can identify what a study's design allows you to validly conclude, including generalizability and causality.
Master Statistics, Data Interpretation, and Distributions on the SAT
These 10 questions are just the start. Unlock the full 1600.lol question bank for 12,000+ official-style SAT questions with the Desmos calculator, instant feedback, and progress tracking.
Join 50,000+ students preparing for the 2025–2026 Digital SAT on 1600.lol