Use this diagnostic to find which Unit 1 topics to revisit: one short question per topic, two for Topics 1.7 and 1.13.
These are original Marlbridge practice questions, not past exam questions, with fictional data. The diagnostic is not calibrated and gives no predicted score.
How to take it. Allow 30 minutes; answer everything before opening any answer. Graphing calculator allowed. Quartiles split the ordered data at the median, leaving the median out of both halves when n is odd. s is the sample standard deviation (divide by n − 1).
Question 1 (multiple choice · 1.1)
An arborist measures the trunk diameter of 32 of a fictional town’s 640 street trees. Which is a datum?
- (A) The 32 trees that were measured
- (B) The trunk diameter of one measured tree, 41 cm
- (C) All 640 street trees in the town
- (D) The list of 32 trunk diameters
Answer and explanation
Answer: (B). A datum is one piece of information about one individual.
- (A) is the sample (n = 32).
- (C) is the population (N = 640).
- (D) is the data set, the whole collection.
If you missed this: Topic 1.1 study guide.
Question 2 (multiple choice · 1.2)
A ferry company recorded four variables for each of its 85 crossings last month. Which is continuous quantitative?
- (A) Number of cars carried
- (B) Crossing time, in minutes
- (C) Weather at departure (calm, breezy or rough)
- (D) Route code, such as 12 or 31
Answer and explanation
Answer: (B). Time is measured; any value in an interval is possible.
- (A) is discrete: cars are counted.
- (C) is categorical: the values are category names.
- (D) is categorical: the numbers are only labels.
If you missed this: Topic 1.2 study guide.
Question 3 (multiple choice · 1.3)
Of 160 visitors to a fictional museum, the relative frequency who arrived by bus was 0.35. Which statement gives the same information?
- (A) 35 of the 160 came by bus.
- (B) 56 came by bus; bus to non-bus is 7 : 13.
- (C) Bus to non-bus is 7 : 20.
- (D) 0.35% came by bus.
Answer and explanation
Answer: (B). 0.35 × 160 = 56 by bus, 104 not; 56 : 104 = 7 : 13.
- (A) is only true when n = 100.
- (C) is part to whole (7 in 20).
- (D) confuses 0.35 with 35%.
If you missed this: Topic 1.3 study guide.
Question 4 (multiple choice · 1.4)
Two fictional towns were asked about a footbridge. In Town A’s pie chart (200 residents) the “Yes” slice is 144°; in Town B’s (500 residents) it is 108°. Which statement is correct?
- (A) A larger proportion said yes in A, but more people said yes in B.
- (B) More people said yes in A, because its slice is larger.
- (C) Pie charts of groups of different sizes cannot be compared.
- (D) A’s larger slice shows that more people were asked there.
Answer and explanation
Answer: (A). Town A: 144 ÷ 360 = 0.40, and 0.40 × 200 = 80. Town B: 108 ÷ 360 = 0.30, and 0.30 × 500 = 150.
- (B) confuses proportion with count.
- (C) is too strong: pies compare proportions well.
- (D) is wrong: every pie is a whole circle, whatever n is.
If you missed this: Topic 1.4 study guide.
Question 5 (multiple choice · 1.5)
Which display of 30 test scores shows the shape and lets a reader recover every score?
- (A) A histogram with bins of width 10
- (B) A stem-and-leaf plot with a key
- (C) A pie chart
- (D) A bar chart with one bar per student, in register order
Answer and explanation
Answer: (B). It shows the shape, and stem plus leaf gives each exact score.
- (A) shows the shape but only counts per bin.
- (C) is for categorical variables.
- (D) shows scores in register order, not the distribution.
If you missed this: Topic 1.5 study guide.
Question 6 (multiple choice · 1.6)
A fictional ferry terminal recorded how long 50 passengers waited. Each bin includes its left edge.
| Wait (minutes) | 0–5 | 5–10 | 10–15 | 15–20 | 20–25 | 25–30 | 30–35 |
|---|---|---|---|---|---|---|---|
| Passengers | 9 | 14 | 6 | 2 | 5 | 11 | 3 |
Which description of the shape is best?
- (A) Bimodal, with peaks at 5–10 and 25–30 minutes
- (B) Skewed right, because the tallest bar is near the left
- (C) Approximately uniform
- (D) Unimodal and approximately symmetric
Answer and explanation
Answer: (A). Two clear peaks (14 and 11) with a dip to 2 between them.
- (B) ignores the second peak.
- (C) is wrong: frequencies run from 2 to 14.
- (D) misses the second peak too.
If you missed this: Topic 1.6 study guide.
Question 7 (multiple choice · 1.7)
A sample has values 4, 7, 7, 9 and 13. What is the sample standard deviation s?
- (A) 2.97
- (B) 3.32
- (C) 11
- (D) 9
Answer and explanation
Answer: (B). x̄ = 40 ÷ 5 = 8. The squared deviations 16, 1, 1, 1 and 25 sum to 44. s² = 44 ÷ 4 = 11, so s = √11 ≈ 3.32.
- (A) divides by n, not n − 1.
- (C) is the variance s².
- (D) is the range, 13 − 4.
If you missed this: Topic 1.7 study guide.
Question 8 (short answer · 1.7)
The delays, in minutes, of 11 trains on a fictional branch line one morning were:
0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 19
(a) Find the median and the IQR. (b) Use the 1.5 × IQR rule to decide whether 19 minutes is a potential outlier. (c) Should the mean or the median describe a typical delay? Justify.
Answer and explanation
(a) The median is the 6th value, 3 minutes. Lower half 0, 1, 1, 2, 2 gives Q1 = 1; upper half 3, 4, 5, 6, 19 gives Q3 = 5. IQR = 4 minutes.
(b) Upper fence = 5 + 1.5 × 4 = 11 minutes. Since 19 > 11, it is a potential outlier.
(c) The median, which is resistant. The outlier pulls the mean up to 46 ÷ 11 ≈ 4.18 minutes, above 8 of the 11 delays.
If you missed this: Topic 1.7 study guide, “Checking for outliers”.
Question 9 (multiple choice · 1.8)
A boxplot of 48 students’ scores on a fictional 15-point test has five-number summary 2, 8, 11, 13, 15 points and no outliers. Which statement is most likely true?
- (A) Skewed left, so the mean is probably below 11 points
- (B) Skewed right, because the left whisker is the longest part
- (C) About half of the students scored from 2 to 8 points
- (D) The mean must be 11 points, like the median
Answer and explanation
Answer: (A). The lower whisker (6) and lower box half (3) are longer than the upper parts (2 and 2): the long tail is toward low scores, which pulls the mean below the median.
- (B) has the direction backwards: skew follows the long tail.
- (C) is wrong: each whisker holds about 25%.
- (D) is wrong: the median does not fix the mean.
If you missed this: Topic 1.8 study guide.
Question 10 (multiple choice · 1.9)
All 900 entrants in a fictional crossword championship had completion times with μ = 64 minutes and σ = 8 minutes. Leena’s time had a z-score of −1.25. What was her time?
- (A) 54 minutes
- (B) 74 minutes
- (C) 62.75 minutes
- (D) 56 minutes
Answer and explanation
Answer: (A). x = μ + zσ = 64 + (−1.25)(8) = 54 minutes.
- (B) adds; negative z means below the mean.
- (C) forgets to multiply by σ.
- (D) is z = −1.
If you missed this: Topic 1.9 study guide.
Question 11 (multiple choice · 1.10)
A fictional company has 6,000 workers. A random number generator selects 300 of them. Those who cycle to work took fewer sick days last year than the rest. Which conclusion is appropriate?
- (A) Generalise to all 6,000 workers; no cause and effect
- (B) Generalise to all 6,000 workers; cycling causes fewer sick days
- (C) Only the 300 workers; cycling causes fewer sick days
- (D) Only the 300 workers; no cause and effect
Answer and explanation
Answer: (A). Random selection allows generalising to the 6,000 workers. Nobody was assigned to cycle, so there is no random assignment: fitness, for example, could affect both cycling and sick days.
- (B) and (C) claim causation without an experiment.
- (D) ignores the random selection.
If you missed this: Topic 1.10 study guide.
Question 12 (multiple choice · 1.11)
A fictional hospital has 1,260 day-shift nurses and 540 night-shift nurses. It wants a stratified random sample of 60 nurses, in proportion to stratum size. How many from each stratum?
- (A) 30 day-shift and 30 night-shift
- (B) 42 day-shift and 18 night-shift
- (C) 126 day-shift and 54 night-shift
- (D) 18 day-shift and 42 night-shift
Answer and explanation
Answer: (B). Day-shift nurses are 1,260 ÷ 1,800 = 0.70 of the staff, and 0.70 × 60 = 42; night-shift nurses get 0.30 × 60 = 18.
- (A) ignores the stratum sizes.
- (C) takes 10% of each stratum: 180 nurses, not 60.
- (D) swaps the strata.
If you missed this: Topic 1.11 study guide.
Question 13 (short answer · 1.12)
To estimate the mean number of films its loyalty-card holders watch there each month, a fictional cinema asks 80 card holders leaving a 9 p.m. Saturday showing.
(a) Name the sampling method and explain why it is likely to be biased. (b) Is the estimate likely to be too high or too low? Why? (c) Describe a better sampling method.
Answer and explanation
(a) A convenience sample. Card holders who rarely visit, or avoid Saturday nights, are unlikely to be asked (undercoverage).
(b) Too high. People at a busy Saturday showing are more likely to be frequent visitors.
(c) Number every card holder on the loyalty-card list and use a random number generator to choose a simple random sample to contact.
If you missed this: Topic 1.12 study guide.
Question 14 (multiple choice · 1.13)
A farm tests two feeds on 40 calves: 20 of breed X and 20 of breed Y. Within each breed, 10 calves are randomly assigned to each feed. What is this design?
- (A) A completely randomized design
- (B) A randomized block design, with breed as the blocking variable
- (C) A matched pairs design
- (D) A stratified random sample
Answer and explanation
Answer: (B). Calves are grouped by breed (the blocks); feeds are randomly assigned within each block.
- (A) would ignore breed when assigning.
- (C) needs pairs, or units getting both treatments.
- (D) is a way of selecting a sample, not of assigning treatments.
If you missed this: Topic 1.13 study guide.
Question 15 (short answer · 1.13)
Thirty-six office workers volunteer. Half will use a standing desk and half a normal desk for a month, then rate their afternoon tiredness from 1 to 10.
(a) Describe how to randomly assign the workers to two equal groups. (b) The standing-desk group reports much lower mean tiredness. What can be concluded, and about whom?
Answer and explanation
(a) Label the workers 01–36. A random number generator picks 18 different labels (ignore repeats); they get standing desks, the other 18 normal desks.
(b) Random assignment means the large difference is evidence that standing desks caused lower tiredness. The workers were volunteers, so this applies only to office workers like them.
If you missed this: Topic 1.13 study guide.
Your next step
| Topic | Question(s) | If you missed it, read |
|---|---|---|
| 1.1 | 1 | Introducing statistics |
| 1.2 | 2 | Variables |
| 1.3 | 3 | Tables for a categorical variable |
| 1.4 | 4 | Graphs for a categorical variable |
| 1.5 | 5 | Graphs for a quantitative variable |
| 1.6 | 6 | Describing distributions |
| 1.7 | 7, 8 | Summary statistics |
| 1.8 | 9 | Boxplots |
| 1.9 | 10 | Comparing distributions |
| 1.10 | 11 | Data collection |
| 1.11 | 12 | Random sampling |
| 1.12 | 13 | Problems with sampling |
| 1.13 | 14, 15 | Experimental design |
How to use your result
- Mark each question right, partly right or wrong. A number with no context is only partly right.
- Fix weak topics in order: boxplots (1.8) use quartiles from 1.7.
- Read the study guide, then do its practice set.
- Then try the Unit 1 mixed review, which combines topics.