What does it mean when an FRQ says 'describe the distribution'?

It signals you should address shape, outliers, center, and spread (SOCS), each stated in the context of the variable and its units. Commit to a specific shape, give numeric values for center and spread, and note any outliers or their absence.

Why do I keep losing points on comparison questions even when my numbers are right?

Comparison rubrics require explicit relational language. Listing two values side by side is not a comparison. Use words like greater than, less than, or more variable, and connect them to the specific statistics and the context of the problem.

Do I have to show the outlier fence calculation, or can I just say a value is an outlier?

Show the calculation. Write the IQR, then the fence such as Q_3 + 1.5 × IQR, and compare the suspect value to it. A conclusion without the supporting fence usually earns only partial credit because the justification is missing.

How much work do I need for a normal-distribution part?

Define the model with its mean and standard deviation, show the z-score computation, report the area or probability, and interpret it as a proportion in context. Skipping the z-score or the context sentence is the most common reason these parts drop from essentially correct to partial.

AP-STATS-1-FRQ

U1 FRQ Practice

Master AP Statistics Unit 1 free-response questions: how to structure answers on distributions, comparisons, boxplots, and normal calculations to earn every point.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on U1 FRQ Practice, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

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What this lesson covers

Unit 1 free-response questions reward clear communication as much as correct computation. The AP exam will hand you a distribution, a set of summary statistics, or two groups to compare, and then judge whether you can describe, interpret, and justify in context. Many students lose points not because they cannot compute a mean or a

z

-score, but because they answer vaguely, forget context, or skip a required comparison word.

This lesson is pure FRQ strategy. You already learned the tools in U1.1 through U1.10; here you learn how graders think, what phrases earn points, and how to structure a response so every part of the rubric is checked off. We will attack shape-center-spread-outliers language, comparison prompts, boxplot construction, and normal-model problems the way the exam actually presents them.

How Unit 1 FRQs Are Structured and Scored

AP free-response questions in Unit 1 typically come in labeled parts, such as (a), (b), and (c), and each part maps to specific rubric points. A part is usually scored as essentially correct (E), partially correct (P), or incorrect (I), and those letters combine into a 0-to-4 score for the whole question.

The single most common way students lose points is failing to answer in context. Graders want the name of the variable and the units, not just abstract statistics. Writing "the center is about 40" is weaker than "the median number of daily customers is about 40."

Rubric expectation	What earns the point	What loses it
Context	Names variable and units	Bare numbers only
Comparison	Uses "greater than," "more than"	Lists two values separately
Justification	Cites specific evidence	States a conclusion only
Completeness	Answers every sub-part	Skips shape or outliers

Read the verb in the prompt. "Describe" asks for shape, center, spread, and outliers. "Compare" requires explicit relational language. "Estimate" or "calculate" expects a number with work shown. Matching your response to the command verb is the fastest way to secure points.

Describing a Single Distribution Under Pressure

When a prompt says "describe the distribution," use SOCS as a checklist: Shape, Outliers, Center, Spread, all in context. On the exam, write in complete sentences and always tie each element to the variable being measured.

For shape, commit to a direction: skewed right, skewed left, roughly symmetric, uniform, or bimodal. If skewed, note that the tail stretches toward the larger or smaller values. For center, report the median or mean with units. For spread, report the range, IQR, or standard deviation, again with units. For outliers, either identify them or state that none are apparent, ideally referencing the

1.5 \times IQR

rule if data allow.

A subtle point graders check: when a distribution is skewed or has outliers, the median and IQR are the preferred resistant measures. If you compute a mean and standard deviation for a strongly skewed distribution without comment, you may still earn the point, but choosing resistant measures shows statistical judgment.

Avoid the phrase "the data is normal" unless the shape is genuinely bell-shaped; "roughly symmetric" is safer and rarely penalized. Also avoid describing center and spread with a single word like "average" that could mean either. Precision in vocabulary is what separates an essentially correct response from a partial one.

Comparing Two Distributions the Right Way

Comparison FRQs are where explicit language matters most. If you write "Group A has a median of 52 and Group B has a median of 45," you have listed, not compared. The rubric wants a relational word: "Group A's median (52 points) is greater than Group B's median (45 points)."

Compare the same features the prompt implies, usually center, spread, and shape, and sometimes outliers. Address each explicitly and in context. A complete comparison paragraph touches all requested characteristics with comparative phrasing for each.

Weak (lists)	Strong (compares)
A is 52, B is 45	A's median is higher than B's
A spreads 20, B spreads 12	A is more variable than B
A is skewed, B symmetric	A is right-skewed while B is symmetric

When comparing from boxplots, remember you can compare medians, IQRs, ranges, and the presence of outliers, but you cannot determine the mean or the exact shape from a boxplot alone. Do not claim shape from a boxplot beyond noting apparent skew based on the relative lengths of the whiskers and box halves. Overclaiming is a common error that turns an essentially correct response into a partial one.

Boxplots, Outliers, and Normal-Model Parts

Some Unit 1 FRQs ask you to construct a boxplot or apply the outlier rule. Show the fence calculation explicitly: lower fence

= Q_1 - 1.5 \times IQR

and upper fence

= Q_3 + 1.5 \times IQR

. Any value beyond a fence is an outlier, and its whisker stops at the most extreme value still inside the fence.

Normal-distribution parts require a labeled process. State the model, standardize, and find the area. For a value

x

from a

N(\mu, \sigma)

distribution, compute

z = \frac{x - \mu}{\sigma}

, then convert to a proportion. Graders look for the

z

-score, the correct probability, and an answer sentence in context.

Step	What to write
1	Define the normal model with $\mu$ and $\sigma$
2	Compute $z = \frac{x-\mu}{\sigma}$
3	Find the area (table or calculator)
4	Interpret as a proportion in context

For "between" problems, subtract the two areas. For "top 10 percent" style problems, work backward: find the

z

with the required area, then solve

x = \mu + z\sigma

. Always show the boundary value and interpret it. Reporting only "0.1587" without saying what proportion of what population it represents can cost the context point.

Key terms

SOCS.: A memory device for describing a distribution: Shape, Outliers, Center, Spread, always stated in context of the variable and units.
Command verb.: The instruction word in a prompt (describe, compare, calculate, justify) that dictates exactly what the rubric expects in your answer.
Resistant measure.: A statistic like the median or IQR that is not strongly affected by outliers or skew, preferred when a distribution is not symmetric.
1.5 IQR rule.: An outlier criterion: values below $Q_1 - 1.5 \times IQR$ or above $Q_3 + 1.5 \times IQR$ are considered outliers.
Comparative language.: Relational phrasing such as greater than, less than, or more variable that the rubric requires on comparison FRQs rather than separate lists.
z-score.: A standardized value $z = \frac{x-\mu}{\sigma}$ giving the number of standard deviations a data point lies from the mean.
Essentially correct (E).: A rubric rating meaning a response fully satisfies the requirements of a question part, contrasted with partially correct (P) or incorrect (I).

Worked example

A researcher records the number of minutes 60 students spend on homework one night. The five-number summary is minimum 10,

Q_1 = 35

, median 50,

Q_3 = 70

, maximum 145. (a) Determine whether 145 is an outlier. (b) Describe the shape of the distribution and justify your reasoning. (c) Assuming for a separate class the homework times are approximately normal with mean 55 minutes and standard deviation 15 minutes, find the proportion of students spending more than 80 minutes.

Part (a): Compute

IQR = Q_3 - Q_1 = 70 - 35 = 35

. The upper fence is

Q_3 + 1.5 \times IQR = 70 + 1.5(35) = 70 + 52.5 = 122.5

. Since

145 > 122.5

, the value 145 is an outlier. Show the fence and the comparison to earn the point.

Part (b): Use the five-number summary to judge skew. The distance from the median to the maximum (

145 - 50 = 95

) is far larger than from the median to the minimum (

50 - 10 = 40

), and the upper whisker and upper half of the data stretch farther. This indicates the distribution of homework times is skewed to the right. Justify with the specific distances, not just an assertion.

Part (c): Model the times as

N(55, 15)

. Standardize the boundary:

z = \frac{80 - 55}{15} = \frac{25}{15} \approx 1.67

. The area to the right of

z = 1.67

is about

1 - 0.9525 = 0.0475

. So approximately 4.75 percent of students in that class spend more than 80 minutes on homework. Include the

z

-score, the area, and the context sentence for full credit.

Practice questions

A prompt asks you to compare the spread of two distributions shown as boxplots. Which response best earns the comparison point?

Distribution X has an IQR of 18 and distribution Y has an IQR of 10.
The IQR of distribution X (18 units) is greater than the IQR of distribution Y (10 units), so X is more variable.
Distribution X is more spread out.
Both distributions have similar centers near 40.

Answer: The IQR of distribution X (18 units) is greater than the IQR of distribution Y (10 units), so X is more variable.

The comparison point requires explicit relational language plus context. The first choice only lists values, the third lacks specific evidence, and the fourth compares center, not spread. The correct choice states the relationship, cites both IQRs, and interprets it as greater variability.

A distribution of house prices is strongly skewed to the right with several high outliers. Which measures of center and spread should you report, and why? Answer in a complete response.

Answer: Report the median as the center and the IQR as the measure of spread because both are resistant to the influence of outliers and skew.

In a right-skewed distribution, the mean is pulled toward the large values and the standard deviation is inflated by outliers, so they misrepresent a typical value and typical spread. The median splits the ordered data in half regardless of extreme values, and the IQR measures the middle 50 percent, both unaffected by the tail. Naming resistance as the reason is what earns the justification point.

Test scores are approximately normal with mean 500 and standard deviation 100. What score marks the top 15 percent of test-takers?

Answer: About 604 points.

Top 15 percent means the area to the right is 0.15, so the area to the left is 0.85. The

z

-score with 0.85 to its left is about 1.04. Solve

x = \mu + z\sigma = 500 + 1.04(100) = 604

. So a score of roughly 604 marks the cutoff. Showing the

z

-value and the back-solving step is required for full credit.

FAQ

What does it mean when an FRQ says 'describe the distribution'?: It signals you should address shape, outliers, center, and spread (SOCS), each stated in the context of the variable and its units. Commit to a specific shape, give numeric values for center and spread, and note any outliers or their absence.
Why do I keep losing points on comparison questions even when my numbers are right?: Comparison rubrics require explicit relational language. Listing two values side by side is not a comparison. Use words like greater than, less than, or more variable, and connect them to the specific statistics and the context of the problem.
Do I have to show the outlier fence calculation, or can I just say a value is an outlier?: Show the calculation. Write the IQR, then the fence such as $Q_3 + 1.5 \times IQR$ , and compare the suspect value to it. A conclusion without the supporting fence usually earns only partial credit because the justification is missing.
How much work do I need for a normal-distribution part?: Define the model with its mean and standard deviation, show the $z$ -score computation, report the area or probability, and interpret it as a proportion in context. Skipping the $z$ -score or the context sentence is the most common reason these parts drop from essentially correct to partial.

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