4.2 Presenting data questions for IB Maths AA

32 questions on Presenting data, 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	15	15
Paper 2	17	17
Every paper	32	32

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-00392Paper 1 · 14 marks

A conservation team catches 200 fish from a lake using nets and measures the length of each fish, in cm. The lengths are summarised in the following table.

Minimum	Lower quartile	Median	Upper quartile	Maximum
9	18	23	27	52

An outlier is a value more than $1.5 \times IQR$ below the lower quartile or above the upper quartile.

(a)
State whether the length of a fish is a discrete or a continuous variable.
1 mark
(b)
Show that the longest fish is an outlier, and that the shortest fish is not.
3 marks
(c)
The longest fish was photographed when it was measured, and it is of a species that is known to grow to more than 60 cm. State, with a reason, whether its length should be kept in the data.
1 mark
(d)
Estimate the number of these 200 fish that are shorter than 27 cm.
2 marks
(e)
The holes in the nets let fish shorter than about 8 cm escape. Explain how this affects the use of these 200 fish to estimate the median length of all the fish in the lake.
1 mark
(f)
The 200 fish are made up of 120 perch, 50 roach and 30 pike. A stratified sample of 40 of these fish, proportional to species, is chosen for further study. Find the number of fish of each species in this sample.
2 marks
(g)
All 200 fish are tagged and returned to the lake. One month later, 150 fish are caught at random from the lake and 12 of them are found to be tagged. Assume that this second catch is a random sample of all the fish in the lake. Estimate the total number of fish in the lake.
3 marks
(h)
State one further assumption needed for the estimate in part (g) to be reliable.
1 mark

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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

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Question 3 · AA-00483Paper 1 · 4 marks

A courier company recorded the delivery times, in hours, of 120 parcels. The results are summarized in the following table, which gives the values used to draw a box and whisker diagram.

Minimum	Lower quartile	Median	Upper quartile	Maximum
12	18	23	30	41

(a)(i)
Write down the range of the delivery times.
1 mark
(a)(ii)
Write down the interquartile range of the delivery times.
1 mark
(b)
Estimate the number of parcels with a delivery time of less than 18 hours or more than 30 hours.
2 marks

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Question 4 · AA-00391Paper 2 · 15 marks

A city council wants to find out about the journey times of the 18 000 people who travel into the city to work each weekday. An officer asks 120 people waiting at the central bus station between 08:00 and 08:30 on one Monday how long their journey to work takes.

(a)
Write down the name of the sampling method used by the officer.
1 mark
(b)
Give two reasons why this sample may not be representative of all the people who travel into the city to work.
2 marks
(c)(i)
The journey times, $t$ minutes, of the 120 people are summarised in the following table.
Journey time, $t$ minutes
Frequency
$0 \leq t < 10$
9
$10 \leq t < 20$
21
$20 \leq t < 30$
34
$30 \leq t < 40$
28
$40 \leq t < 50$
17
$50 \leq t < 60$
8
$60 \leq t < 70$
3
Find an estimate of the mean and an estimate of the standard deviation of the journey times.
3 marks
(c)(ii)
Write down the class interval that contains the median journey time.
1 mark
(c)(iii)
One of these 120 people is chosen at random. Find the probability that their journey time is at least 40 minutes.
1 mark
(d)(i)
The officer also kept the exact journey times. For these 120 values, the lower quartile is 21 minutes and the upper quartile is 39 minutes. An outlier is a value more than $1.5 \times IQR$ above the upper quartile or below the lower quartile.
Find the least journey time that would be an outlier.
2 marks
(d)(ii)
The longest journey time in the sample is 68 minutes. State, with a reason, whether this value should be removed from the data.
2 marks
(e)(i)
The following week, the council takes a systematic sample of 150 people from a list of the 15 000 people who hold a monthly travel pass for the city.
Find the sampling interval.
2 marks
(e)(ii)
Explain why this sample may still not represent all the people who travel into the city to work.
1 mark

Journey time, $t$ minutes	Frequency
$0 \leq t < 10$	9
$10 \leq t < 20$	21
$20 \leq t < 30$	34
$30 \leq t < 40$	28
$40 \leq t < 50$	17
$50 \leq t < 60$	8
$60 \leq t < 70$	3

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Question 5 · AA-00484Paper 1 · 6 marks

The 80 runners who took part in a 10 km fun run each recorded their finishing time, $t$ minutes. The following cumulative frequency graph shows the results, with $t$ on the horizontal axis and the cumulative frequency on the vertical axis.

cumulative frequency

Cumulative frequency of finishing times, t minutes

(a)
Write down the median finishing time.
1 mark
(b)
Find the interquartile range of the finishing times.
2 marks
(c)
The slowest 10% of the runners took longer than $k$ minutes. Find the value of $k$ .
3 marks

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Question 6 · AA-00418Paper 2 · 5 marks

The finishing times, $t$ minutes, of the 400 runners in a fun run are summarized in the following table.

Time ( $t$ minutes)	Number of runners
$t < 30$	18
$30 \leq t < 40$	64
$40 \leq t < 50$	121
$50 \leq t < 60$	97
$60 \leq t < 75$	72
$75 \leq t < 90$	28

A runner is selected at random. Let $L$ be the event "the runner finished in less than 50 minutes" and let $M$ be the event "the runner took at least 40 minutes".

(a)
Given that the runner finished in less than 50 minutes, find the probability that the runner finished in less than 40 minutes.
2 marks
(b)
Determine whether the events $L$ and $M$ are independent. Justify your answer.
3 marks

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