Weights: $Q_1=135\text{ g}$, median $=190\text{ g}$, $Q_3=242\text{ g}$, max $=390\text{ g}$. Is $390$ an outlier?

1. IQR : $Q_3 - Q_1 = 242 - 135 = 107\text{ g}$. 2. Upper boundary : $Q_3 + 1.5 \times \text{IQR} = 242 + 1.5(107)$. 3. Evaluate : $242 + 160.5 = 402.5\text{ g}$. 4. Compare : $390 < 402.5$. 5. Conclude : $390\text{ g}$ is not an outlier .

The mean of five distinct positive integers is $8.4$ . Find the sum of these five integers. A sixth integer, $x$ , is added to the data set. The new mean of all six integers is exactly $9$ . Find the value of $x$ . Two different classes took a mathematics test. Class A has 20 students and achieved a mean score of 65 marks. Class B has 30 students and achieved a mean score of 80 marks. Calculate the combined mean score for all 50 students.

Sum $= 5 \times 8.4$ (M1) $= 42$ A1 New total $= 6 \times 9 = 54$ (M1) $x = 54 - 42 = 12$ A1 Combined total $= 20(65) + 30(80) = 1300 + 2400 = 3700$ M1 Combined mean $= \frac{3700}{50} = 74$ A1

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IB Maths AI SL · Unit 4: Statistics and Probability

IB Maths AI SL Descriptive Statistics Questions

Q: How many IB Maths AI SL descriptive statistics questions are there?

There are 36 exam-style descriptive statistics questions in the AI SL question bank (Paper 1: 21 · Paper 2: 15), graded 7 easy, 19 medium, 5 hard, 5 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Q: Is descriptive statistics on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 21 · Paper 2: 15. Practise with your GDC — AI papers expect calculator methods throughout.

Q: Where can I get the mark schemes?

Open the AI 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 AI SL descriptive statistics 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.

36 questions
Paper 1: 21
Paper 2: 15
7 easy
19 medium
5 hard
5 very hard
3 worked examples

Practise Descriptive Statistics questions →

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

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1 of 5

Question 1 of 5
Question 2 of 5
Question 3 of 5
Question 4 of 5
Question 5 of 5

Start with one question on mean, median and mode. Stuck? Take a hint. No sign-in needed.

Find the mean of

4, 7, 7, 9, 13

Choose your answer · keys 1–4

10

8

7

40

Find the mean of the data in the table.

$x$	10	20	30
Frequency	3	5	2

Choose your answer · keys 1–4

19

20

\frac{190}{3}

\frac{10}{3}

$x$	2	4	6	8
Frequency	1	4	4	1

What's examined in AI SL descriptive statistics

The question bank covers these descriptive statistics question types (number of questions in brackets):

Data measures and calculations (16)
Visual data representations (12)
Effects of data transformations (8)

Key formulas

Interquartile range: $IQR = Q_{3} - Q_{1}$
Mean of a data set: $\bar{x} = \frac{\sum_{i = 1}^{n} f_{i} x_{i}}{n}, n = \sum f_{i}$

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

Explained, with a worked example: Standard deviation

Descriptive Statistics worked examples

Worked example 1: Mean, median, and mode · easy

Goals scored in seven matches: $4, 6, 6, 8, 11, 12, 16$ . Write down the mode and median, and calculate the exact mean.

Solution

5 steps · 1 to fill in

Examiner tip: With an even number of values, the median is the mean of the two middle numbers. Always sort first!

Worked example 2: Testing for outliers · medium

Weights: $Q_{1} = 135 g$ , median $= 190 g$ , $Q_{3} = 242 g$ , max $= 390 g$ . Is $390$ an outlier?

Solution

5 steps · 1 to fill in

Examiner tip: The lower boundary is

Q_{1} - 1.5 \times IQR

. Memorise both — they are not in the formula booklet.

Worked example 3: Mean from grouped frequency data · hard

$60$ commuter distances: $[0, 10)$ : 4, $[10, 20)$ : 11, $[20, 30)$ : 25, $[30, 40)$ : 16, $[40, 50)$ : 4. Estimate the mean to 3 s.f.

Solution

5 steps · 1 to fill in

Examiner tip: It is an "estimate" because we assume every commuter travelled exactly the mid-interval distance.

Try these IB Maths AI SL descriptive statistics 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 · 6 marks · Paper 1

The daily wait times, in minutes, for a bus are recorded over 8 days: $5, 12, 14, 15, 18, 21, 24, 45$

Find the lower quartile ( $Q_{1}$ ) and the upper quartile ( $Q_{3}$ ) of the wait times.
Calculate the interquartile range (IQR).
Determine if the wait time of $45$ minutes is considered an outlier. Show all your working.

Attempt it and see the mark scheme →

Question 2 · medium · 6 marks · Paper 2

The mean of five distinct positive integers is $8.4$ .

Find the sum of these five integers.
A sixth integer, $x$ , is added to the data set. The new mean of all six integers is exactly $9$ . Find the value of $x$ .
Two different classes took a mathematics test. Class A has 20 students and achieved a mean score of 65 marks. Class B has 30 students and achieved a mean score of 80 marks. Calculate the combined mean score for all 50 students.

Full worked solution Free, no sign-in

Sum $= 5 \times 8.4$ (M1)
$= 42$ A1
New total $= 6 \times 9 = 54$ (M1)
$x = 54 - 42 = 12$ A1
Combined total $= 20 (65) + 30 (80) = 1300 + 2400 = 3700$ M1
Combined mean $= \frac{3700}{50} = 74$ A1

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

Question 3 · hard · 6 marks · Paper 1

The five numbers in a dataset, arranged in ascending order, are: $x, x + 2, 2 x - 3, 2 x + 1, 3 x - 4$ The median of this dataset is $11$ .

Find the value of $x$ .
Hence, list the five numbers in the dataset.
Calculate the mean of the dataset.

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All 36 descriptive statistics questions with mark schemes →

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FAQ

How many IB Maths AI SL descriptive statistics questions are there?

There are 36 exam-style descriptive statistics questions in the AI SL question bank (Paper 1: 21 · Paper 2: 15), graded 7 easy, 19 medium, 5 hard, 5 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is descriptive statistics on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 21 · Paper 2: 15. Practise with your GDC — AI papers expect calculator methods throughout.

Where can I get the mark schemes?

Open the AI 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.

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Teaching this topic?

Free ready-to-teach lesson (slides and teacher notes): Measures of spread (SD, IQR).

IB Maths AI SL Descriptive Statistics Questions

Try it first

What's examined in AI SL descriptive statistics

Key formulas

Descriptive Statistics worked examples

Worked example 1: Mean, median, and mode · easy

Solution

Worked example 2: Testing for outliers · medium

Solution

Worked example 3: Mean from grouped frequency data · hard

Solution

Try these IB Maths AI SL descriptive statistics questions

Question 1 · easy · 6 marks · Paper 1

Question 2 · medium · 6 marks · Paper 2

Full worked solution Free, no sign-in

Question 3 · hard · 6 marks · Paper 1

Revise descriptive statistics for the exam

FAQ

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Teaching this topic?

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