Quiz 7 — Data and Simulation (Lectures 25–28)

Time: 20 minutes · Closed book · Answer all questions.

Q1. Choosing a summary (4 marks)

A library records daily visits. One month's data contains: typical days around 200 visits, plus two exam-week days with 900 visits each.

(a) Which summary — mean or median — better represents a typical day here? Justify in one sentence. (2) (b) Give one question about this data for which the mean is the right summary despite the outliers. (2)

Q2. Percentages and bases (4 marks)

A notice claims: "Attendance rose 50% this year! Last year 40 students attended the workshop."

(a) How many attended this year? (1) (b) The same notice later says "Attendance fell 50% the year before last." Why can the two percentages not be chained as "back to where we started" without care? (2) (c) One sentence: what must every percentage statement carry to be checkable? (1)

Q3. Simulation design (6 marks)

Two friends flip a fair coin; heads the first wins 1 from the second, tails the second wins 1 from the first. They stop when one of them is broke. The first starts with 2 coins, the second with 3. You must estimate, by simulation, the probability that the first friend ends with all 5 coins.

(a) Describe one trial of the simulation precisely: what is random, what is recorded, when does the trial end? (3) (b) Name two decisions in the design that must be fixed before running, and say why. (2) (c) The estimate from 10 trials is 0.4 and from 10,000 trials is 0.3987. Which do you report, and why, in one sentence? (1)

Q4. Cleaning rules (6 marks)

A spreadsheet of workshop sign-ups has columns name, email, year. Defects found: 3 rows with missing email; 5 rows with year = 99; 2 rows that are exact duplicates of other rows; 1 row where name is "TEST".

(a) Classify each defect: drop, fix, or investigate-first — with a one-line justification each. (4) (b) State the general rule this table illustrates about deleting data. (2)