4.1 Populations, samples and sampling questions for IB Maths AA

18 questions on Populations, samples and sampling, written by Augment in the style of IB exam papers. Six of them are below in full, to answer on paper.

IB Mathematics: Analysis and Approaches
Part of 4 Statistics and probability
SL and HL

Questions by paper and level

SL and HL questions are for students at either level. HL only questions cover what only HL students study.

Paper	SL and HL	All
Paper 1	9	9
Paper 2	9	9
Every paper	18	18

Counted on 10 November 2026

Questions to try

Written by Augment in the style of IB exams, not past papers. Answer them on paper, then check each one against its markscheme with a free account.

Question 1 · AA-00383Paper 1 · 5 marks

A sports centre has 1440 members. Each member holds exactly one type of membership, as shown in the following table.

Membership type	Junior	Adult	Senior
Number of members	360	864	216

The manager wants to survey a sample of 60 members. She decides to use a stratified sample, with the number chosen from each membership type proportional to the number of members of that type.

(a)
Find the number of junior, adult and senior members in the sample.
3 marks
(b)
State one advantage of this stratified sample compared with a simple random sample of 60 members.
1 mark
(c)
The survey asks each selected member for
- the number of visits they made to the centre last month;
- the length of time they spent in the centre on their most recent visit.
State whether each of these variables is discrete or continuous.
1 mark

The markschemeCheck this one with a free account

Question 2 · AA-00385Paper 2 · 6 marks

A biology student grows 12 tomato seedlings for three weeks and then records the height of each seedling, in cm. The recorded heights are shown below.

0.6 4.8 5.2 5.5 5.9 6.1 6.4 6.6 7.0 7.3 7.9 11.8

A value is considered an outlier if it is more than $1.5 \times IQR$ below the lower quartile or more than $1.5 \times IQR$ above the upper quartile.

(a)
Find the lower quartile and the upper quartile of the recorded heights.
2 marks
(b)
Show that $0.6$ and $11.8$ are both outliers.
2 marks
(c)
Every seedling was at least $3$ cm tall when it was planted at the start of the three weeks. For each of the two outliers, state whether it should be kept in or removed from the data, giving a reason.
2 marks

The markschemeCheck this one with a free account

Question 3 · AA-00384Paper 1 · 6 marks

A bakery produces 1500 loaves of bread each day. The loaves leave the oven one at a time on a conveyor belt and are numbered 1 to 1500 in the order in which they leave. A quality inspector wants to check a sample of 60 loaves each day using systematic sampling.

(a)
Describe how the inspector should select the sample.
2 marks
(b)
On one day the randomly chosen starting loaf is loaf number 7. Write down the number of the fourth loaf selected.
1 mark
(c)
Find the probability that a particular loaf is selected on that day.
1 mark
(d)
The loaves are baked on trays that each hold exactly 25 loaves, and they leave the oven in the same order every day. Loaves baked in the corner position of a tray are more likely to be overcooked.
Explain why the systematic sample may give a misleading estimate of the proportion of overcooked loaves.
2 marks

The markschemeCheck this one with a free account

Question 4 · AA-00389Paper 2 · 6 marks

A courier records the masses, in kg, of nine parcels delivered on one morning.

2.40 3.85 1.95 31.5 2.70 4.10 2.25 3.30 2.85

(a)(i)
For the recorded masses, find the mean.
1 mark
(a)(ii)
For the recorded masses, find the standard deviation.
1 mark
(b)
The courier then discovers that the mass of $31.5$ kg was a recording error, and that the true mass of this parcel was $3.15$ kg. Find the mean and the standard deviation of the nine true masses.
2 marks
(c)
State, with a reason, whether correcting the error changes the median mass.
2 marks

The markschemeCheck this one with a free account

Question 5 · AA-00386Paper 1 · 4 marks

A market researcher stands in the main hall of a railway station and asks passengers to complete a questionnaire. She has been instructed to obtain 20 responses from each of the age groups 18–29, 30–49 and 50 and over. She asks whichever passengers she chooses, and stops asking people in an age group once she has 20 responses from that group.

(a)
Write down the name of this sampling method.
1 mark
(b)
Explain why this sample is not a random sample.
1 mark
(c)
The questionnaire asks each passenger for the number of train journeys they made last week and the total distance, in km, that they travelled by train last week.
State whether each of these two variables is discrete or continuous.
2 marks

The markschemeCheck this one with a free account

Question 6 · AA-00390Paper 2 · 14 marks

A town has 6400 households. An energy company selects a simple random sample of 250 of these households. Of the households in the sample, 48 have solar panels.

(a)
Estimate the number of households in the town that have solar panels.
2 marks
(b)(i)
The daily electricity use, $E$ kWh, of each household in the sample is recorded. The results are shown in the following table.
Daily use, $E$ kWh
Number of households
$0 \leq E < 5$
18
$5 \leq E < 10$
52
$10 \leq E < 15$
85
$15 \leq E < 20$
61
$20 \leq E < 25$
26
$25 \leq E < 30$
8
Write down the modal class.
1 mark
(b)(ii)
Find an estimate of the mean and an estimate of the standard deviation of the daily electricity use.
3 marks
(c)
Estimate the number of households in the town that use at least 20 kWh per day.
2 marks
(d)
The company contacts 12 households in the town, chosen at random. Assume that the proportion of all households in the town with solar panels is the same as the proportion in the sample. Find the probability that at least 3 of the 12 households have solar panels.
3 marks
(e)
State one assumption required for the model used in part (d).
1 mark
(f)
An employee suggests that it would have been quicker to survey the 250 households that live closest to the company's office. Give two reasons why this would be likely to give less reliable estimates than the random sample.
2 marks

Daily use, $E$ kWh	Number of households
$0 \leq E < 5$	18
$5 \leq E < 10$	52
$10 \leq E < 15$	85
$15 \leq E < 20$	61
$20 \leq E < 25$	26
$25 \leq E < 30$	8

The markschemeCheck this one with a free account

Practice all 18 in Augment

Free with an account. Every question has its markscheme, and Augment keeps the ones you got wrong so you can come back to them.

Start free Log in

The notes on 4.1 Populations, samples and sampling

Check your answers in Augment

A free account opens all 18 questions on Populations, samples and sampling with their markschemes, and keeps a record of what you have marked.

Start free

Questions by paper and level

Questions to try

Practice all 18 in Augment

More questions in Statistics and probability

Check your answers in Augment