AP Statistics Unit 1 FRQ Practice: Free Response Questions

Free Response Question · Unit 1 · Describing Data & Sampling

A researcher wants to study how many hours per week students at a large high school spend on homework. She records the values for a group of students and computes the five-number summary (in hours) shown below. The distribution has a mean of about 10.5 hours.

Statistic	Value (hours)
Minimum	2
Q1	6
Median	9
Q3	13
Maximum	28

Describe the shape, center, and spread of this distribution, justifying the shape using the given values.

✓ Model answer

The distribution appears skewed to the right: the maximum (28) is much farther above Q3 than the minimum (2) is below Q1, and the mean (10.5) is greater than the median (9), which is typical of right skew. A reasonable measure of center is the median, 9 hours. For spread, the IQR = Q3 − Q1 = 13 − 6 = 7 hours (and the range is 28 − 2 = 26 hours).

Why it scores: Names the shape (right-skewed) AND justifies it (mean > median, long upper tail), reports the center, and gives a numerical measure of spread. Because the data are skewed, using the median and IQR is the appropriate choice.

Use the 1.5 × IQR rule to determine whether the maximum value of 28 hours is an outlier. Show your work.

✓ Model answer

IQR = 13 − 6 = 7, so 1.5 × IQR = 10.5. The upper fence is Q3 + 1.5·IQR = 13 + 10.5 = 23.5 hours. Since 28 > 23.5, the maximum value of 28 hours is an outlier. (The lower fence is 6 − 10.5 = −4.5, so the minimum of 2 is not a low outlier.)

Why it scores: Computes the IQR and the upper fence explicitly, compares 28 to the fence, and states the conclusion. Simply calling 28 an outlier because it "looks big" would not earn credit — the 1.5 × IQR calculation is required.

The researcher collected her data by surveying only students she found in the school library after school. Identify the sampling method, explain a likely source of bias, and describe how it would affect her estimate of the average homework time for all students at the school.

✓ Model answer

This is a convenience sample — she chose students who were easy to reach rather than selecting randomly. A likely source of bias is undercoverage: students who spend time in the library after school are probably more studious than the overall student body, and students who never use the library have no chance of being selected. As a result, her sample would tend to include heavier homework-doers, so her estimate of the average homework time would most likely be biased too high — an overestimate — and it should not be generalized to all students at the school.

Why it scores: Names the method (convenience sample), identifies a specific bias (undercoverage of non-library students), AND states the direction of the effect (overestimate) with reasoning. A vague answer like "the sample is biased" without the direction and reason would lose credit.

How to score points on AP Statistics FRQs

Answer in context. Refer to the actual variable (homework hours) and population (all students at the school), not just generic "data."
Justify the shape. Cite the relationship between the mean and median, or the relative tail lengths — don't just assert "skewed right."
Show every calculation. For outliers, write the IQR, the fences, and the comparison — a bare conclusion earns nothing.
Name the direction of bias. Say whether an estimate is too high or too low and explain why.
Match statistic to shape. Use the median and IQR for skewed data; the mean and standard deviation for roughly symmetric data.