An economist compared annual household income, in thousands of dollars, for an independent random sample of 75 households in Region E with an independent random sample of 77 households in Region F, and displayed the results in the histograms shown below. A student claims that the mean income is higher than the median income in both regions. Is this claim reasonable based on the histograms?
AP Statistics · Unit 1 · Exploring One-Variable Data and Collecting Data
174 AP-style multiple-choice questions and 8 free-response questions for AP Statistics · Unit 1 · Exploring One-Variable Data and Collecting Data, sorted into 9 topics. Free sample questions for every topic.
9 topics174 multiple-choice8 free-response
Topic 1 of 9
comparing distributions of a quantitative variable
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A survey asked a random sample of customers at two coffee shops to rate their visit on a five-point scale, with results summarized in the frequency table below.
| Rating | Shop 1 (n=60) | Shop 2 (n=60) |
|---|---|---|
| 1 | 3 | 8 |
| 2 | 7 | 12 |
| 3 | 12 | 18 |
| 4 | 20 | 15 |
| 5 | 18 | 7 |
Based on this table, which of the following best compares the two shops' distributions of ratings?
Sample free-response question
A courier company recorded the delivery times, in minutes, for 10 randomly selected deliveries on each of two routes.
| Route | Delivery times (minutes) |
|---|---|
| North | 12, 15, 15, 16, 18, 19, 21, 22, 24, 38 |
| South | 14, 16, 17, 17, 18, 18, 19, 20, 20, 21 |
(a) Calculate the median delivery time for each route. Show your work.
(b) Is the North delivery time of 38 minutes an outlier? Justify your answer using the 1.5 x IQR rule. The North quartiles are Q1 = 15 and Q3 = 22.
(c) Compare the distributions of delivery times for the two routes. Address center and variability, in context.
(d) The company wants deliveries that rarely take a long time. Which route should it choose? Explain using the comparisons in part (c).
16 more questions on this topic
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Answer, then see why
The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?
Not quite. The answer is B.
Why the other options are wrong
AI grading for free-response
Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.
Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sureReason: Correctly identifies demand for gasoline as inelastic.
Evidence: "The price of gasoline rises and the quantity falls only a little."
Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."