4.3 Measures of central tendency and dispersion questions for IB Maths AA

48 questions on Measures of central tendency and dispersion, 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	23	23
Paper 2	25	25
Every paper	48	48

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-00403Paper 1 · 6 marks

In an experiment, a student heats samples of water to different temperatures, $y$ °C, and measures the mass of a salt, $x$ grams, that dissolves in each sample.

The regression line of $x$ on $y$ is $x = 0.45 y + 3.2$ , and Pearson's product-moment correlation coefficient is $0.88$ . The mean of the masses is $21.2$ grams.

(a)
Find the mean of the temperatures.
2 marks
(b)
The student later finds that the thermometer was faulty, and every temperature recorded was 5 °C too high. Each temperature is corrected by subtracting 5 °C. The masses are unchanged.
Find the equation of the regression line of $x$ on $y$ for the corrected data.
3 marks
(c)
Write down the value of Pearson's product-moment correlation coefficient for the corrected data.
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-00406Paper 1 · 13 marks

The 40 members of an athletics club each record their best time for a 5 km race, $x$ minutes, and their best time for a 10 km race, $y$ minutes.

For these data, the regression line of $y$ on $x$ is $y = 2.1 x - 0.5$ and the regression line of $x$ on $y$ is $x = 0.4 y + 4.2$ .

(a)
Find the mean 5 km time and the mean 10 km time of the members.
4 marks
(b)
Find the sum of the 10 km times of all 40 members.
1 mark
(c)
Interpret, in context, the value $2.1$ in the regression line of $y$ on $x$ .
1 mark
(d)
Ana's best 5 km time is 22 minutes. Use an appropriate regression line to estimate her best 10 km time.
2 marks
(e)
Ben's best 10 km time is 60 minutes. Use an appropriate regression line to estimate his best 5 km time.
2 marks
(f)
Ana reduces her best 5 km time by 3 minutes. Estimate the change in her best 10 km time.
1 mark
(g)
By writing the regression line of $x$ on $y$ in the form $y = m x + k$ , show that the two regression lines are different. State what this tells you about the value of Pearson's product-moment correlation coefficient, $r$ .
2 marks

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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

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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-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

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