Week 3 — Quiz (auto-graded) · Center & Spread

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective tested: Objective 2 — summarize univariate data: center (mean/median/mode) and spread (variance, SD, IQR, five-number summary).
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 3.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-03-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 3 misconceptions named in the lecture outline. All arithmetic is pre-computed and double-checked.

Questions, key, and feedback

Q1 (MC). Find the mean of these five values: 4, 6, 8, 10, 12.
- A. 6
- B. 8 ✅
- C. 10
- D. 40
Feedback: Add them (4+6+8+10+12 = 40) and divide by the count (5): 40 ÷ 5 = 8. (Distractor D = the total, before dividing.)

Q2 (MC). Find the median of these five values: 3, 5, 8, 9, 20.
- A. 5
- B. 8 ✅
- C. 9
- D. 20
Feedback: Sorted, the middle (3rd) of five values is 8. (The mean here is 9 — distractor C — because the value 20 pulls the average up; the median ignores how far away it is.)

Q3 (Multiple answer — select all that apply). Which of the following statements are true?
- A. The mean is found by adding all values and dividing by how many there are ✅
- B. The median is the value that occurs most often
- C. The median is the middle value once the data is sorted ✅
- D. The mode is the only measure of center that works for categorical data ✅
- E. The mean is never affected by an outlier
Feedback: A, C, and D are correct. The median is the middle value (B describes the mode), and the mean is dragged by outliers (E is false). (B swaps median and mode; E is the "mean ignores extremes" misconception.)

Q4 (MC). A neighborhood's five home prices (in $1000s) are 22, 24, 25, 27, 180. Which measure of center best represents a typical home here?
- A. The mean, because it uses every value
- B. The median, because the data is skewed by one expensive home ✅
- C. The mode, because prices repeat
- D. The range, because it shows the spread
Feedback: One very expensive home makes the data right-skewed (mean ≈ $55.6k vs. median $25k), so the median is the honest summary. (A = the "mean is always right" trap; the mean sits above four of the five homes.)

Q5 (MC). What does the standard deviation of a dataset measure?
- A. The most common value
- B. The middle value
- C. How spread out the values are around the mean ✅
- D. The difference between the largest and smallest values
Feedback: The SD is roughly the typical distance of a value from the mean — a measure of spread, not center. (D describes the range; A and C-vs-B confuse spread with the mode/median.)

Q6 (Matching). Match each measure to its description.
| Measure | Correct description |
|---|---|
| Mean | Add all values and divide by how many there are |
| Median | The middle value once the data is sorted |
| Mode | The value that occurs most often |
| IQR | Q3 − Q1 — the spread of the middle 50% of the data |
Feedback: Mean = add and divide; Median = the middle of the sorted line; Mode = the most frequent value; IQR = the distance between the third and first quartiles.

Q7 (MC). Seven exam scores, sorted, are 4, 7, 9, 12, 15, 16, 22. Their five-number summary is Min = 4, Q1 = 7, Median = 12, Q3 = 16, Max = 22. What is the IQR?
- A. 18
- B. 9 ✅
- C. 12
- D. 5
Feedback: IQR = Q3 − Q1 = 16 − 7 = 9 (the spread of the middle 50%). (A = the range, Max − Min = 22 − 4 = 18 — the classic range-vs-IQR mix-up.)

Q8 (True / False). "A larger standard deviation means the dataset has a higher average (center)."
- True
- False ✅
Feedback: False. The SD measures spread, not center. Two datasets can share the same mean and have very different standard deviations.

Q9 (MC). A dataset is 15, 16, 17, 18, 19 (mean 17, median 17). One value, 19, is changed to 99. What happens?
- A. Both the mean and the median jump up a lot
- B. The mean jumps up a lot (to 33), but the median stays 17 ✅
- C. The median jumps up a lot, but the mean stays 17
- D. Neither the mean nor the median changes
Feedback: The mean uses every value, so the outlier drags it from 17 to 33; the median depends only on position, so it stays 17. The median is resistant; the mean is not.

Q10 (MC). Compute the sample standard deviation of 2, 2, 4, 6, 6. (Mean = 4; squared deviations 4, 4, 0, 4, 4 sum to 16.)
- A. 4
- B. 2 ✅
- C. 16
- D. 8
Feedback: Sample variance = sum of squared deviations ÷ (n − 1) = 16 ÷ 4 = 4; the SD is √4 = 2. (A = the variance, before the square root; C = the sum of squares.)

Answer key (quick reference)

Quality gate (self-checked): every single-answer item has exactly one correct option; the multiple-answer item (Q3) lists the three true statements (A, C, D); all arithmetic was pre-computed and verified — Q1 mean = 8, Q2 median = 8, Q4 mean 55.6 vs. median 25, Q7 IQR = 16 − 7 = 9, Q9 new mean = 33 / median = 17, Q10 sample SD = √(16÷4) = 2. No item asserts a fact outside the Week 3 course definitions.

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

All ten items are tagged course=MATH11 · week=3 · objective=2 · topic=center-and-spread and deposited in Item Bank: Week 3 — Center & Spread. The midterm (Week 8) and the per-term variant updates draw fresh items from this bank. (Tags: q1 mean-compute, q2 median-compute, q3 center-definitions, q4 mean-vs-median-skew, q5 sd-meaning, q6 measure-matching, q7 iqr-compute, q8 sd-misconception, q9 resistance, q10 sd-compute.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 3 Quiz — Center & Spread"
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"