These are original Marlbridge practice questions, not past exam questions. All places, organisations and data are fictional. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. Conventions for every question: N is the population size and n is the sample size; round percentages to 1 decimal place. A basic calculator is enough.
Question 1 (multiple choice · foundation)
The town of Corvel has 14 running clubs with 1,350 adult members in total. A sports-drink company wants to know how much water these club members drink on a training day. It picks 90 members from the clubs’ combined membership list and asks each of them.
What is the population in this study?
- (A) The 90 members who were asked
- (B) All 1,350 adult members of Corvel’s running clubs
- (C) All adults who live in Corvel
- (D) The amounts of water drunk by the 90 members
Answer and explanation
Answer: (B). The question is about members of Corvel’s running clubs, so the population is all of them: N = 1,350.
- (A) is the sample (n = 90), the part of the population that data were collected from.
- (C) is too wide. The company’s question is about club members, not every adult in the town.
- (D) is the data set: the information recorded. The population is the individuals, not their answers.
Question 2 (multiple choice · foundation)
Which of these is an investigative question that needs a statistical investigation to answer it?
- (A) What time does the first lesson start at Elmstead School?
- (B) How many floors does the Elmstead School main building have?
- (C) How long do Year 11 students at Elmstead School typically spend on homework on a weeknight?
- (D) What was the temperature at the Elmstead School gate at 8 a.m. today?
Answer and explanation
Answer: (C). Homework time differs from student to student, so you need data from many students and a summary such as a typical value. That is a statistical investigation.
- (A) has one fixed answer that you can look up in the timetable. No variability is involved.
- (B) is answered by a single count. The answer is a number, but it does not vary across individuals.
- (D) is a single measurement at one place and time. One reading answers it.
Question 3 (multiple choice · core)
A factory in Dunmore made 12,000 phone chargers last week. Inspectors test 250 of them by running each one at full power until it fails. Which statement is correct?
- (A) N = 12,000 and n = 250
- (B) N = 250 and n = 12,000
- (C) N = 12,250 and n = 250
- (D) n = 250 ÷ 12,000 ≈ 0.02
Answer and explanation
Answer: (A). The population is all 12,000 chargers made last week, so N = 12,000. The sample is the 250 chargers tested, so n = 250. As always, n is less than N.
- (B) swaps the symbols. Capital N is for the population; lower-case n is for the sample.
- (C) adds the sample to the population. The 250 tested chargers are already part of the 12,000.
- (D) is the fraction of the population sampled (about 2%), not the sample size. The sample size is a count.
Question 4 (multiple choice · core)
A researcher planned to answer: “What proportion of customers at Pellow Market buy fruit on a weekday visit?” After analysing her data, she found the proportion was small. She then changed her question to “What proportion of customers who stay longer than 30 minutes buy fruit?” and reported a much larger proportion from the same data.
Which is the best criticism of what she did?
- (A) The investigative question should be fixed before the analysis; changing it after seeing the results lets the data choose the question, so the report can mislead.
- (B) There is no problem, because both questions use the same data set.
- (C) The only problem is that the new question uses a smaller n, so the calculation is harder.
- (D) An investigative question should never mention a population.
Answer and explanation
Answer: (A). A valid investigative question has a defined purpose that is set at the start and is not changed because of the analysis. Switching questions until the result looks interesting gives a misleading picture of the evidence.
- (B) misses the point. Using the same data does not make it acceptable to pick the question after seeing the results.
- (C) notices a real side effect (fewer customers stay longer than 30 minutes) but not the main problem, which is changing the question after the analysis.
- (D) is false. A good investigative question should make the population clear.
Question 5 (constructed response · core)
A wildlife charity studies a fictional bird, the Tarn swallow, on Harrow Isle. About 3,000 adult Tarn swallows live on the island. The charity wants to know the mean wingspan of these birds. Volunteers catch 40 adult birds, measure each wingspan, and release them. The total of the 40 wingspans is 1,260 cm.
(a) Write the investigative question for this study. (b) Identify the population, N, the sample and n. (c) Give an example of one datum, and describe the data set. (d) Calculate the mean wingspan of the birds measured and state it in context.
Worked solution and suggested Marlbridge rubric
(a) “What is the mean wingspan of adult Tarn swallows living on Harrow Isle?”
(b) Population: all adult Tarn swallows on Harrow Isle, N ≈ 3,000. Sample: the 40 adult birds caught and measured, n = 40.
(c) One datum is the wingspan of one bird, for example “32 cm”. The data set is the list of 40 wingspans, one for each bird measured.
(d) Mean = 1,260 ÷ 40 = 31.5 cm. In context: the 40 adult Tarn swallows measured on Harrow Isle had a mean wingspan of 31.5 cm.
| Point | What earns it |
|---|---|
| 1 | An investigative question that names the population (adult Tarn swallows on Harrow Isle) and what is wanted (mean wingspan) |
| 1 | Correct population with N ≈ 3,000 and correct sample with n = 40 |
| 1 | A datum as one bird’s wingspan with units, and the data set as all 40 wingspans |
| 1 | Mean 31.5 cm with a statement naming the birds, the variable (wingspan) and the unit |
Do not award point 2 if the sample is described as “the 1,260 cm” or if N and n are swapped. For point 4, “the mean is 31.5” with no context does not earn the point.
Question 6 (constructed response · core)
Students at Oakridge School are planning a project about the school canteen. They suggest three investigative questions:
- “Is the canteen food good?”
- “What did Priya eat for lunch on Monday?”
- “What proportion of students at Oakridge School buy lunch from the canteen on a typical school day?”
(a) For each question, say whether it is a valid investigative question for a statistical study. Give a reason for each. (b) Rewrite one of the invalid questions so that it is valid.
Worked solution and suggested Marlbridge rubric
(a)
- Question 1: not valid. “Good” is not defined, and no population is named. There is no clear purpose and no way to know what data to collect.
- Question 2: not valid. It is about one person on one day. One answer settles it, so it does not need a statistical investigation.
- Question 3: valid. It names the population (students at Oakridge School), what to record for each student (buys canteen lunch or not), and the answer comes from data that vary across students.
(b) One possible rewrite of question 1: “What is the typical rating, on a scale of 1 to 10, that Oakridge School students give to the canteen’s main meals?” Another for question 2: “What proportion of Oakridge School students ate a hot lunch on Monday?”
| Point | What earns it |
|---|---|
| 1 | Question 1 not valid, with a reason about the undefined word “good” or the missing population |
| 1 | Question 2 not valid because one individual/one answer means no statistical investigation is needed; and question 3 valid with a reason |
| 1 | A rewrite that names a population, says what will be recorded for each individual, and needs data that vary |
Accept other sensible rewrites. A rewrite that is still about one person, or that still uses an undefined word such as “good” or “nice”, does not earn point 3.
Question 7 (explanation · stretch)
The city of Valden has 86,000 households. The city council asked 500 households whether they have solar panels on their home; 115 said yes. A news reporter wrote:
“Exactly 23% of households in Valden have solar panels, so 19,780 households in the city have them.”
(a) Give N and n for this study, and show that the sample percentage is 23%. (b) Write a correct statement of the result in context. (c) Explain what is wrong with the word “exactly” in the reporter’s statement. (d) Give one reason the council asked a sample of households rather than every household.
Model answer and suggested Marlbridge rubric
(a) N = 86,000 households; n = 500 households. 115 ÷ 500 = 0.23 = 23%.
(b) 115 of the 500 Valden households asked (23%) said they have solar panels on their home.
(c) The 23% describes only the 500 households in the sample. A different sample of 500 households would probably give a slightly different percentage, so the true percentage for all 86,000 households is not known exactly. The reporter’s figure of 19,780 households (0.23 × 86,000) is an estimate, not an exact count, and it is only a fair estimate if the sample represents the city well.
(d) Contacting all 86,000 households would take a lot of time and money, and many would not reply. Asking 500 is much quicker and cheaper.
| Point | What earns it |
|---|---|
| 1 | N = 86,000 and n = 500, with 115 ÷ 500 = 23% shown |
| 1 | A statement that names the 500 households asked, solar panels and the percentage |
| 1 | Explains that the sample value describes the sample and would vary from sample to sample, so it is not exactly the city value |
| 1 | A sensible reason (time, cost, difficulty of reaching every household) linked to this context |
For point 3, “the reporter might be wrong” with no reason does not earn the point. A response must say that the value comes from a sample and samples vary.
How did you do?
- Q1 or Q3 wrong: re-read “The parts of a statistical study” in the study guide. Population = everything the question is about; N for the population, n for the sample.
- Q2 or Q6 wrong: revisit “What makes a good investigative question?” and Worked example 2.
- Q4 wrong: revisit “Fix the question before you look at the results” in the same section.
- Q5 wrong: work through Worked example 1 again, especially the datum and the statement in context.
- Q7 incomplete: revisit “Writing in context”. A sample result describes the sample; another sample would give a slightly different value.
Then tick off the topic checklist.