Week 2 — Quiz (auto-graded) · Summarizing Data with Tables & Graphs

Course: Introduction to Statistics (18-week generic edition)
Objective tested: Objective 2 — frequency & relative-frequency tables; choosing and reading displays; distribution shape; misleading graphs.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Week 2 · Closed to AI.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-02-qti.xml; the reusable item-bank entries and the Canvas placement block are at the bottom of this file.

Blueprint

The table below maps each item to its type and concept.

No trick questions; distractors target the Week 2 misconceptions named in the lecture outline.

Questions, key, and feedback

Q1 (MC). A price-tracking app checks the price of regular gasoline at 50 stations across one metro area and sorts each station's price into a class. 12 stations fall in the $3.40–<$3.60 class. What is the relative frequency of that class?
- A. 0.12
- B. 0.24 ✅
- C. 0.76
- D. 4.17
Feedback: Relative frequency = count ÷ total = 12 ÷ 50 = 0.24. (A treats 12 as if the total were 100; C subtracts from 1 for no reason; D divides the wrong way, 50 ÷ 12.)

Q2 (MC). A relative-frequency table of the movie runtimes at one theater lists shares of 0.15, 0.35, and 0.30 — and one final class whose entry is smudged and unreadable. What must the smudged relative frequency be?
- A. 0.10
- B. 0.80
- C. 0.20 ✅
- D. 0.25
Feedback: All relative frequencies sum to 1: 0.15 + 0.35 + 0.30 = 0.80, so the missing share is 1 − 0.80 = 0.20. (B is the sum of the three shown — the "forgot to subtract" trap.)

Q3 (Multiple answer — select all that apply). Which of the following displays are appropriate for a quantitative variable, such as a resident's daily step count?
- A. Histogram ✅
- B. Pie chart
- C. Dot plot ✅
- D. Stem-and-leaf plot ✅
- E. Bar chart of separated category bars
Feedback: Quantitative values live on a number line, so the displays that use one — histogram, dot plot, stem plot — all work. A pie needs parts of one whole; separated category bars have no number line at all.

Q4 (MC). A histogram of the daily step counts of 40 walking-challenge participants has these classes and frequencies: 4,000–<6,000 steps: 6 people; 6,000–<8,000: 14; 8,000–<10,000: 12; 10,000–<12,000: 8. How many participants logged fewer than 8,000 steps?
- A. 14 people
- B. 26 people
- C. 20 people ✅
- D. 32 people
Feedback: Add the classes entirely below 8,000: 6 + 14 = 20. (B adds the wrong pair, 14 + 12; D is 40 − 8.)

Q5 (MC). A city's restaurant inspection scores run 0–100. Most restaurants score in the high 80s and 90s, while a few score far lower. The distribution of scores is —
- A. Symmetric, because the bulk of the scores land close to one another
- B. Skewed to the right, because the tall peak sits at the high scores
- C. Uniform, because scores are free to land anywhere from 0 up to 100
- D. Skewed to the left, because the thin tail stretches toward the low scores ✅
Feedback: Skew is named for the tail, never the peak. The long thin tail runs toward the low scores — skewed left. (B is the classic peak-side error: the tail tells the tale.)

Q6 (Matching). Match each display to what it shows.

The table below pairs each display with its correct description.

Q7 (MC). A gas-station chain's ad shows a bar chart comparing its average regular price, $3.45, with a competitor's $3.55 — but the vertical axis starts at $3.40. What makes the chart misleading?
- A. The truncated axis makes a 10-cent gap look like the competitor charges roughly triple ✅
- B. Bar charts are only allowed to display counts, never dollar amounts like prices
- C. Prices are parts of one whole, so the data belonged in a pie chart instead
- D. Nothing — starting the axis at $3.40 just trims empty space from the picture
Feedback: Drawn from a floor of $3.40, the bars rise 0.05 vs. 0.15 — a visual 3× — while the honest ratio is 3.55 ÷ 3.45 ≈ 1.03, about 3% more. Bar length encodes value, so bar axes start at zero.

Q8 (True / False). If a dot plot of daily step counts shows one value far above all the rest, the correct first move is to delete that value so it doesn't distort the graph.
- True
- False ✅
Feedback: False. An outlier is a flag, not garbage: investigate first — a real value stays (and gets reported); an error gets fixed and documented. Silent deletion is never the move.

Q9 (MC). A streaming dashboard displays 60 movie runtimes using separated bars sorted from tallest to shortest, like a bar chart. What's the problem?
- A. Runtime is quantitative, so the bars belong in number-line order, touching ✅
- B. Runtime is categorical, so the slices belong in a pie that totals 100%
- C. The display is fine, because any variable can use separated, sorted bars
- D. The bars are correct but should run from the shortest to the tallest
Feedback: Runtimes live on a number line, so their display is a histogram: touching bars in fixed number-line order. Sorting by height scrambles the line. Bars apart = categories; bars touching = a number line.

Q10 (MC). A fitness app tallies how many of its 2,000 users earned each of four activity badges last month. Users can earn several badges, so the four counts add to more than 2,000. Why is a pie chart the wrong display for these counts?
- A. Pie charts cannot display as many as four different slices at once
- B. Pie charts require quantitative data, and badge counts are categorical
- C. A pie chart would work fine here, because every count is a percentage
- D. The badge counts overlap, so the slices wouldn't be parts of one whole ✅
Feedback: A pie is legal only for non-overlapping parts of one whole summing to 100%. Overlapping counts (one user in several slices) don't form a whole — use a bar chart.

Answer key (quick reference)

The table below is the quick-reference key.

Quality gate (self-checked): each single-answer item has exactly one correct option; the multiple-answer item's three number-line displays are the only quantitative-appropriate options listed; all arithmetic re-verified (12 ÷ 50 = 0.24; 1 − 0.80 = 0.20; 6 + 14 = 20; 0.15 ÷ 0.05 = 3 and 3.55 ÷ 3.45 ≈ 1.03); no positional pattern in the key (B C · C D · A · A D) and no letter carries more than two of the seven MC items; no length giveaway (options within each item are comparable lengths); no item asserts a fact outside the Week 2 course definitions; no scenario reuses the tutorial, practice, chapter, lab, or assignment surfaces.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged week=2 · objective=2 · topic=tables-and-graphs and deposited in Item Bank: Week 2 — Summarizing Data with Tables & Graphs with idents w02q1–w02q10. The midterm (Week 9), the final (Week 18), and per-term variant updates draw fresh variants from this bank's concepts — never these live stems. (Tags: w02q1 relative-frequency, w02q2 shares-sum-to-1, w02q3 quantitative-displays, w02q4 histogram-reading, w02q5 skew-direction, w02q6 display-matching, w02q7 truncated-axis, w02q8 outlier-policy, w02q9 bar-vs-histogram, w02q10 pie-legality.)

Canvas placement block

canvas_object    = Quizzes::Quiz
title            = "Week 2 Quiz — Summarizing Data with Tables & Graphs"
assignment_group = "Quizzes"
points_possible  = 10
grading_type     = points
due_offset_days  = 6        # end of the module's week
published        = true
shuffle_answers  = true