Week 2 — Quiz (auto-graded) · Summarizing Data

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective tested: Objective 2 — summarize and display univariate data (frequency & relative-frequency tables; histograms; shape; outliers).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 2.

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

No trick questions; distractors target the Week 2 misconceptions named in the lecture outline (reading bars as frequencies vs. ranges; the "skewed right" direction trap; an outlier's effect on the mean and on the shape; relative frequency changing the shape).

All arithmetic in this quiz is pre-computed from the Week 2 lecture-outline data sets and verified below in the quality gate.

Questions, key, and feedback

Q1 (MC). A class surveys the commute times (minutes) of 30 students and groups them into classes of width 10. The frequency table reads: 0–9 → 9 students; 10–19 → 13; 20–29 → 6; 30–39 → 2. Which class is the modal class (the most common commute)?
- A. 0–9 minutes
- B. 10–19 minutes ✅
- C. 20–29 minutes
- D. They are all equally common
Feedback: The modal class is the one with the biggest count — 13 students fall in 10–19, the tallest bar. (A "frequency" is just a count; the largest count names the peak.)

Q2 (MC). Using the same table (9, 13, 6, 2 over 30 students), what share of students commute under 20 minutes?
- A. 22%
- B. About 73% ✅
- C. About 43%
- D. About 27%
Feedback: Relative frequency = frequency ÷ total. Under 20 min = 9 + 13 = 22 students, and 22 ÷ 30 = 0.733 ≈ 73%. (Distractor A reports the raw count, 22, as if it were a percent — the count-vs-share confusion.)

Q3 (Multiple answer — select all that apply). Which of the following are true of a histogram (and help distinguish it from a bar chart)?
- A. Its bars touch, with no gaps between them ✅
- B. The bars can be reordered to look tidier (e.g., tallest first)
- C. The horizontal axis is a number line (quantitative data) ✅
- D. Each bar's height is the count (or share) of values in that class ✅
- E. It is the right display for a categorical variable like blood type
Feedback: A histogram shows quantitative data on a number line, so its bars touch and the order is fixed; each height is the class's count. Reordering bars (B) and categorical data (E) belong to bar charts. (Bars touch → histogram; bars apart → bar chart.)

Q4 (MC). For which variable is a histogram (not a bar chart) the correct display?
- A. Students' declared majors
- B. Favorite streaming service
- C. Daily high temperatures for a month ✅
- D. Eye color
Feedback: Histograms are for quantitative data (numbers on a number line) — daily high temperatures qualify. Majors, streaming service, and eye color are categorical → bar chart. (Quantitative → histogram, bars touch; categorical → bar chart, bars apart.)

Q5 (MC). On a histogram of commute times, the bar over the class 10–19 minutes rises to a height of 13. What does that 13 mean?
- A. The longest commute in that group is 13 minutes
- B. The commute times in that bar add up to 13
- C. 13 students had a commute between 10 and 19 minutes ✅
- D. The bar is 13 minutes wide
Feedback: A bar's height is the frequency — the count of values that fall in its class (the range is shown by the bar's width on the axis). So 13 means 13 students landed in 10–19 min. (Reading the height as a value, a width, or a sum is the classic "bars are ranges, heights are counts" mix-up.)

Q6 (Matching). Match each distribution shape to the picture that fits it.
| Shape | Correct description |
|---|---|
| Symmetric | One central hump; the left and right halves are rough mirror images |
| Skewed right | Tall bars on the left, a long thin tail stretching toward the large values |
| Skewed left | Tall bars on the right, a long thin tail stretching toward the small values |
| Uniform | All bars about the same height; no real peak |
Feedback: Skew is named for the tail: a tail trailing toward big values is skewed right; toward small values, skewed left. Symmetric = mirror halves; uniform = flat (a fair die). (Bimodal — two separate humps — is the fifth shape from the outline.)

Q7 (MC). A histogram of home prices in a city has its tall bars on the left (most homes are moderately priced) and a long thin tail stretching to the right toward a few very expensive homes. This distribution is —
- A. Skewed left
- B. Skewed right ✅
- C. Symmetric
- D. Uniform
Feedback: The tail points right (toward the big values), so it is skewed right — even though the tall bulk sits on the left. (Distractor A is the #1 trap: naming the skew for where the hump is instead of where the tail goes.)

Q8 (True / False). "Switching a histogram from frequency to relative frequency changes the shape of the distribution."
- True
- False ✅
Feedback: False. Dividing every height by the total only relabels the vertical axis; the bars keep the same relative heights, so the shape is identical. Relative frequency just lets you compare groups of different sizes.

Q9 (MC). Nine employees' years of experience are 31, 33, 34, 35, 36, 37, 38, 40, 120 (the 120 is a data-entry slip). The mean is 44.9 years and the median is 36 years. Drop the erroneous 120 and recompute: the mean becomes 35.5 and the median becomes 35.5. What does this show?
- A. Removing a value always changes the median more than the mean
- B. The outlier dragged the mean far more than the median — the mean is sensitive, the median is resistant ✅
- C. The outlier had no real effect on either summary
- D. The median is the value most affected by an outlier
Feedback: Dropping the 120 moved the mean by 9.4 years (44.9 → 35.5) but the median by only 0.5 (36 → 35.5). The mean chases the outlier; the median holds its ground. (The mean adds every value; the median only cares about position.)

Q10 (MC). A data set of typical household incomes has one billionaire accidentally included. What does this single extreme value do to a histogram of the data?
- A. Nothing — a histogram is immune to outliers
- B. It makes the distribution look perfectly symmetric
- C. It stretches the horizontal axis to reach the far value, squashing all the real data into a few bins on the left ✅
- D. It adds a tall bar in the middle of the graph
Feedback: One far-out value forces the axis to stretch to include it, compressing the real data into a sliver on the left — the histogram loses its shape and looks misleadingly empty. (Notice and report the outlier's effect; don't let it silently distort the picture.)

Answer key (quick reference)

Quality gate (self-checked):
- Exactly one correct option on every single-answer item (Q1, Q2, Q4, Q5, Q7, Q9, Q10); the true/false (Q8) keys to False; the multiple-answer item (Q3) lists exactly the three true histogram statements (A, C, D) and excludes the two bar-chart statements (B, E); the matching item (Q6) pairs all four shapes one-to-one.
- Arithmetic pre-computed and verified against the Week 2 lecture-outline data:
- Commute table counts 9 + 13 + 6 + 2 = 30 ✓; modal class = 10–19 (count 13) ✓.
- Under-20 share = (9 + 13) ÷ 30 = 22 ÷ 30 = 0.733 ≈ 73% ✓.
- Employee mean with 120 = 404 ÷ 9 = 44.9 ✓; median = 36 ✓. Without 120: mean = 284 ÷ 8 = 35.5 ✓; median = (35 + 36)/2 = 35.5 ✓; mean shift = 9.4, median shift = 0.5 ✓.
- No item asserts a fact outside the Week 2 course definitions (frequency/relative frequency, histogram vs. bar chart, the five shapes, skew named for the tail, outlier sensitive/resistant).

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

All ten items are tagged course=MATH11 · week=2 · objective=2 · topic=summarizing-data and deposited in Item Bank: Week 2 — Summarizing Data. The midterm (Week 8) and the per-term variant updates draw fresh items from this bank. (Tags: q1 frequency-table, q2 relative-frequency, q3 histogram-properties, q4 histogram-vs-barchart, q5 reading-histogram-bar, q6 shapes, q7 skew-direction, q8 relative-frequency-shape, q9 outlier-mean-median, q10 outlier-histogram.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 2 Quiz — Summarizing Data"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start
published       = true
shuffle_answers = true
provenance      = "~ Prof. Rivera's edition · Fall 2026 · built with thecoursemaker.com"