A box-and-whisker plot summarizes a set of data. The minimum value is $12$, the lower quartile is $25$, the median is $38$, the upper quartile is $52$, and the maximum value is $95$. Calculate the interquartile range (IQR). Determine mathematically whether the maximum value of $95$ should be classified as an outlier.

$\text{IQR} = Q_3 - Q_1 = 52 - 25$ (M1) $\text{IQR} = 27$. A1 Upper outlier boundary: $Q_3 + 1.5 \times \text{IQR} = 52 + 1.5(27) = 92.5$. M1 Since $95 > 92.5$, the maximum value $95$ is an outlier. R1

Home › IB Maths AA SL › Questions by topic › Presentation of Data

IB Maths AA SL · Unit 4: Statistics and Probability

IB Maths AA SL Presentation of Data Questions

Q: How many IB Maths AA SL presentation of data questions are there?

There are 43 exam-style presentation of data questions in the AA SL question bank (Paper 1: 33 · Paper 2: 10), graded 15 easy, 17 medium, 8 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Q: Is presentation of data on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 33 · Paper 2: 10. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Q: Where can I get the mark schemes?

Open the AA SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

Updated October 2026

Exam-style IB Maths AA SL presentation of data questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step, showing the working that earns the marks — then try the practice questions and check your working against the mark scheme.

43 questions
Paper 1: 33
Paper 2: 10
15 easy
17 medium
8 hard
3 very hard
3 worked examples

Practise Presentation of Data questions →

🖩 How do I do this on my calculator? Keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire.

What's examined in AA SL presentation of data

The question bank covers these presentation of data question types (number of questions in brackets):

Data Organisation & Summaries (21)
Box Plot Analysis (14)
Cumulative Frequency Graphs (8)

Key formulas

Mean of a data set: $\bar{x} = \frac{\sum f_{i} x_{i}}{n}, n = \sum f_{i}$

In the same notation as the IB formula booklet. All AA SL formulas →

Presentation of Data worked examples

Worked example 1: Reading box-and-whisker plots · easy

Five-number summary: min $0$ , $Q_{1} = 11$ , median $14$ , $Q_{3} = 19$ , max $39$ . Find IQR and determine if $32$ is an outlier.

Solution

3 steps · 1 to fill in

Examiner tip: Show the numerical boundary value AND the inequality comparison (

32 > 31

) to secure the reasoning mark.

Worked example 2: Analyzing cumulative frequency curves · medium

Cumulative frequency curve for $80$ students, passing through $(15, 14), (16.5, 20), (20, 40), (23.5, 60)$ . Find median, IQR, and number below 15 min.

Solution

4 steps

Examiner tip: The vertical axis is the NUMBER of data points, not percentages. Quartile positions use

N

(the highest CF), not

100

Worked example 3: Outlier boundaries and unknowns · hard

IQR $= 20$ , no outliers, max $= 75$ . Find the minimum possible upper quartile $U$ .

Solution

3 steps

Examiner tip: Translating "no outliers" into an inequality (max

\leq

boundary) is the key higher-order move here.

Try these IB Maths AA SL presentation of data questions

Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.

Question 1 · easy · 4 marks · Paper 1

State whether the following variables are discrete or continuous:

The exact mass of an apple.
The number of pages in a novel.
The length of a wooden ruler.
The shoe sizes of students in a class.

Attempt it and see the mark scheme →

Question 2 · medium · 4 marks · Paper 1

A box-and-whisker plot summarizes a set of data. The minimum value is $12$ , the lower quartile is $25$ , the median is $38$ , the upper quartile is $52$ , and the maximum value is $95$ .

Calculate the interquartile range (IQR).
Determine mathematically whether the maximum value of $95$ should be classified as an outlier.

Full worked solution Free, no sign-in

$IQR = Q_{3} - Q_{1} = 52 - 25$ (M1)
$IQR = 27$ . A1
Upper outlier boundary: $Q_{3} + 1.5 \times IQR = 52 + 1.5 (27) = 92.5$ . M1
Since $95 > 92.5$ , the maximum value $95$ is an outlier. R1

Every question here has a full worked solution. See them all →

Question 3 · hard · 5 marks · Paper 1

A histogram is drawn to represent a continuous data set. The data is divided into three equal class intervals: $0 \leq x < 10$ , $10 \leq x < 20$ , and $20 \leq x < 30$ . The frequencies for these intervals are $p$ , $2 p$ , and $p$ respectively, where $p$ is a positive integer.

By using the mid-interval values and summing algebraically, prove that the estimated mean of this dataset is exactly $15$ , regardless of the value of $p$ .
Explain why the standard deviation of this dataset will also be independent of the value of $p$ .

Attempt it and see the mark scheme →

Free account — sign in to download Topic PDF: 7 questions with worked answers · 5 pages · 172 KB

All 43 presentation of data questions with mark schemes →

Save your progress and get 5 more questions on every topic, checked instantly. Free account, no card. Join free

Revise presentation of data for the exam

FAQ

How many IB Maths AA SL presentation of data questions are there?

There are 43 exam-style presentation of data questions in the AA SL question bank (Paper 1: 33 · Paper 2: 10), graded 15 easy, 17 medium, 8 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is presentation of data on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 33 · Paper 2: 10. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Where can I get the mark schemes?

Open the AA SL Unit 4 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

What else is free here

Save your answers and track your progressA free account remembers the questions you have done on every topic and brings you back to this page.

Join free

Already have an account? Sign in

Teaching this topic?

Free ready-to-teach lessons (slides and teacher notes): Sampling techniques & bias · Measures of spread (SD, IQR).

IB Maths AA SL Presentation of Data Questions

Try it first

What's examined in AA SL presentation of data

Key formulas

Presentation of Data worked examples

Worked example 1: Reading box-and-whisker plots · easy

Solution

Worked example 2: Analyzing cumulative frequency curves · medium

Solution

Worked example 3: Outlier boundaries and unknowns · hard

Solution

Try these IB Maths AA SL presentation of data questions

Question 1 · easy · 4 marks · Paper 1

Question 2 · medium · 4 marks · Paper 1

Full worked solution Free, no sign-in

Question 3 · hard · 5 marks · Paper 1

Revise presentation of data for the exam

FAQ

What else is free here

Teaching this topic?

More AA SL Unit 4 topics