4.2 Presenting data questions for IB Maths AI

27 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: Applications and Interpretation
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	13	13
Paper 2	14	14
Every paper	27	27

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 · AI-00197Paper 1 · 7 marks

As part of a road-safety study, 40 drivers each take a computer test that measures their reaction time, in seconds. The results are summarised in the following table.

Minimum	Lower quartile	Median	Upper quartile	Maximum
0.09	0.24	0.27	0.31	0.44

(a)
Write down the interquartile range.
1 mark
(b)
Determine whether the minimum and the maximum are outliers.
4 marks
(c)
The researchers know that no person can genuinely react to the test in less than 0.1 seconds. Comment on whether each of the two outliers should be kept in the data.
2 marks

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Question 2 · AI-00198Paper 2 · 18 marks

Lindiwe's farm has three apple orchards. The numbers of apple trees in each orchard are shown in the following table.

Orchard	Hillside	Riverbank	Valley
Number of trees	1840	1150	1010

Lindiwe wants to check 80 trees for disease.

(a)
She decides to use a stratified sample. Find the number of trees she should check in each orchard.
3 marks
(b)
Explain why a stratified sample may be more suitable than a simple random sample of 80 trees.
1 mark
(c)
Lindiwe also weighs apples. State whether the mass of an apple is discrete or continuous data.
1 mark
(d)
The masses, in grams, of 12 apples picked from Riverbank are:
$142, 156, 161, 148, 170, 152, 165, 139, 158, 147, 163, 236$
Find
(i) the mean mass;
(ii) the standard deviation of the masses.
3 marks
(e)
(i) Find the lower quartile, the median and the upper quartile of the masses.
(ii) Show that the mass of 236 g is an outlier.
6 marks
(f)
Draw a box-and-whisker diagram to represent the masses of the 12 apples, using a horizontal scale from 120 g to 240 g.
3 marks
(g)
Lindiwe checks her notebook and confirms that the 236 g apple was weighed correctly. State, with a reason, whether she should remove it from the data.
1 mark

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Question 3 · AI-00376Paper 1 · 7 marks

The times taken by 160 runners to complete a 5 km park run are shown on the following cumulative frequency curve.

Cumulative frequency curve of the times of 160 runners. Horizontal axis: time in minutes from 16 to 40. Vertical axis: cumulative frequency from 0 to 160. The curve passes through (16, 0), (20, 12), (24, 46), (28, 98), (32, 134), (36, 152) and (40, 160).

(a)
Use the cumulative frequency curve to estimate
(i) the median time;
(ii) the lower quartile;
(iii) the upper quartile;
(iv) the interquartile range.
4 marks
(b)
Estimate the number of runners who took more than 30 minutes.
2 marks
(c)
Write down the number of runners who took between 24 and 28 minutes.
1 mark

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Question 4 · AI-00703Paper 2 · 16 marks

A forester measures the heights of 240 young pine trees in a plantation. The results are shown on the following cumulative frequency curve.

Cumulative frequency curve of the heights of 240 trees. Horizontal axis: height in m from 4 to 20. Vertical axis: cumulative frequency from 0 to 240. The curve passes through (4, 0), (6, 6), (8, 22), (10, 58), (12, 112), (14, 168), (16, 208), (18, 232) and (20, 240).

(a)
Use the curve to estimate the median height.
1 mark
(b)
Use the curve to estimate the interquartile range of the heights.
3 marks
(c)
The shortest tree has a height of 5.2 m. Determine whether this height is an outlier.
3 marks
(d)
Use the curve to complete the following frequency table.
Height ( $h$ m)
$4 < h \leq 6$
$6 < h \leq 8$
$8 < h \leq 10$
$10 < h \leq 12$
$12 < h \leq 14$
$14 < h \leq 16$
$16 < h \leq 18$
$18 < h \leq 20$
Frequency
6
16
56
24
8
2 marks
(e)
Use your table to find an estimate of
(i) the mean height;
(ii) the standard deviation of the heights.
3 marks
(f)
The forester models the height of a tree in the plantation, $H$ m, by $H \sim N (12.3, {3.2}^{2})$ . Use this model to estimate the number of the 240 trees that are taller than 16 m.
3 marks
(g)
Use the cumulative frequency curve to comment on the accuracy of your answer to part (f).
1 mark

Height ( $h$ m)	$4 < h \leq 6$	$6 < h \leq 8$	$8 < h \leq 10$	$10 < h \leq 12$	$12 < h \leq 14$	$14 < h \leq 16$	$16 < h \leq 18$	$18 < h \leq 20$
Frequency	6	16			56		24	8

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Question 5 · AI-00377Paper 1 · 7 marks

Rangi records the lengths, in cm, of the trout he catches in a lake during one season. The lengths are shown in the following box-and-whisker diagram.

Box-and-whisker diagram of trout lengths on a scale from 20 cm to 50 cm. Minimum 22, lower quartile 31, median 35, upper quartile 38, maximum 46.

(a)
Write down the median length.
1 mark
(b)
Find the interquartile range.
2 marks
(c)
Find the greatest length that a trout could have without being an outlier.
2 marks
(d)
Rangi's friend catches a trout of length 20 cm in the same lake. Assuming the quartiles do not change, determine whether this length would be an outlier.
2 marks

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Question 6 · AI-00704Paper 2 · 17 marks

A health authority records the waiting times, in minutes, of 12 randomly chosen patients at each of two clinics, A and B.

Clinic A	18	22	25	27	29	31	32	34	36	38	41	47
Clinic B	12	15	17	19	20	22	23	24	26	28	31	52

The waiting times for clinic A are shown in the following box-and-whisker diagram.

Box-and-whisker diagram for Clinic A on a scale of waiting time from 10 to 55 minutes: minimum 18, lower quartile 26, median 31.5, upper quartile 37, maximum 47. The row for Clinic B is empty.

(a)
For the waiting times at clinic B, write down
(i) the median;
(ii) the lower quartile and the upper quartile.
3 marks
(b)
Show that the waiting time of 52 minutes at clinic B is an outlier.
2 marks
(c)
On the same scale as the diagram, draw a box-and-whisker diagram for the waiting times at clinic B.
3 marks
(d)
Make two comparisons between the waiting times at the two clinics.
2 marks
(e)
The health authority wants to test, at the 5% significance level, whether the mean waiting time at clinic B is less than at clinic A. It assumes that the waiting times at each clinic are normally distributed with equal variances.
Write down the null and alternative hypotheses.
2 marks
(f)
Find the $p$ -value for the test.
2 marks
(g)
State the conclusion of the test. Give a reason for your answer.
2 marks
(h)
With reference to your diagram for clinic B, comment on the assumption that the waiting times at clinic B are normally distributed.
1 mark

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