SAT Statistics, Data Interpretation, and Distributions: 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
Statistics questions emphasize interpretation. The mean is affected by extreme values, while the median is more resistant. The mode is the most frequently occurring value. In a symmetric distribution the mean and median align; in a right-skewed distribution the mean is generally above the median, and in a left-skewed distribution it is generally below.
Measures of spread describe dispersion. Range is max - min. A larger standard deviation means values are more spread out around the mean. Interquartile range, Q3 - Q1, describes the middle 50% and is resistant to extreme values.
Data interpretation can use bar charts, line graphs, scatterplots, histograms, and two-way tables. Read the axis scale and legend before comparing values. For a scatterplot, use the given line of best fit to estimate a value or describe the direction of a trend, staying within the model's stated context.
A distribution may be symmetric, left-skewed, or right-skewed. Use its visible shape and any given summary statistics rather than assuming a real-world variable follows a particular distribution.
Key Rules & Formulas
Memorize these rules — they come up directly in practice 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?
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Correct answer: D. 16
Explanation
Mean = (14 + 16 + 15 + 17 + 18) / 5 = 80 / 5 = 16.
Seven test scores are listed in order: 62, 70, 74, 81, 85, 90, 93. What is the median score?
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Correct answer: C. 81
Explanation
The median is the middle value of the ordered list. With 7 values, the 4th value is the median: 81.
A dataset has values: 5, 8, 8, 10, 12, 14, 14, 14, 20. Which measure of center is greatest?
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Correct answer: B. Mode
Explanation
Mean = (5+8+8+10+12+14+14+14+20)/9 = 105/9 ≈ 11.67. Median = 12 (5th value). Mode = 14. The mean (≈11.67) is less than the median (12) and mode (14). The mode 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?
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Correct answer: A. 57
Explanation
Original total = 20 × 78 = 1,560. New total needed for mean of 77 with 21 students = 21 × 77 = 1,617. New student's score = 1,617 − 1,560 = 57.
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?
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Correct answer: D. 5–9
Explanation
With 50 employees, the median is between the 25th and 26th values. Cumulative: 0–4 has 12; adding 5–9 gives 30. The 25th and 26th values both fall in the 5–9 interval.
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?
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Correct answer: C. Class B has greater spread than Class A
Explanation
Standard deviation measures spread. Class B has a larger standard deviation (12 > 8), so Class B has greater spread. Both means are equal (75).
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?
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Correct answer: B. 95
Explanation
Substitute x = 10: y = 4(10) + 55 = 40 + 55 = 95.
A dataset has a mean of 50 and a median of 42. Which of the following best describes the likely shape of the distribution?
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Correct answer: A. Skewed right (mean > median)
Explanation
When the mean > median, the distribution is skewed right—the tail extends toward the higher values, pulling the mean above the median.
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?
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Correct answer: D. Both mean and range
Explanation
Increasing the largest value increases the sum of all values, so the mean increases: new mean = (200 + 10)/10 = 21. The range also increases because the maximum value is now 10 larger: new range = 15 + 10 = 25. Both 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?
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Correct answer: B. Maximum
Explanation
Adding a value of 95, which is greater than the current maximum of 80, will raise the maximum to 95. The median, Q1, and Q3 may or may not change depending on the full data distribution, but the maximum will definitely increase.
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Common Mistakes to Avoid
Use this checklist to catch common traps while working through Statistics, Data Interpretation, and Distributions questions, then add your own patterns as you review missed answers.
- !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)
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 test
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
Continue with this skill in the question bank, or test how it holds up under section timing before returning to the surrounding Problem Solving skills.