IB Maths AA SL · Unit 4: Statistics and Probability
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 the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
The question bank covers these presentation of data question types (number of questions in brackets):
Five-number summary: min $0$, $Q_1 = 11$, median $14$, $Q_3 = 19$, max $39$. Find IQR and determine if $32$ is an outlier.
1. IQR: $Q_3 - Q_1 = 19 - 11 = \mathbf{8}$.
2. Upper boundary: $Q_3 + 1.5 \times \text{IQR} = 19 + 12 = 31$.
3. Compare: $32 > 31$, so $32$ is a mathematical outlier.
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.
1. Median at CF $= 40$: $\mathbf{20}$ min.
2. $Q_1$ at CF $= 20$: $16.5$; $Q_3$ at CF $= 60$: $23.5$.
3. IQR: $23.5 - 16.5 = \mathbf{7}$ min.
4. Below 15 min: from $(15, 14)$, $\mathbf{14}$ students.
IQR $= 20$, no outliers, max $= 75$. Find the minimum possible upper quartile $U$.
1. Upper boundary: $U + 1.5(20) = U + 30$.
2. No-outlier condition: max $\le$ boundary, so $75 \le U + 30$.
3. Solve: $U \ge 45$; minimum $= \mathbf{45}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
State whether the following variables are discrete or continuous:
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 $95$.
A histogram is drawn to represent a continuous data set. The data is divided into three equal class intervals: \(0 \le x < 10\), \(10 \le x < 20\), and \(20 \le x < 30\). The frequencies for these intervals are \(p\), \(2p\), 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 \(p\).
There are 25 exam-style presentation of data questions in the AA SL question bank (Paper 1: 17 · Paper 2: 8), graded 9 easy, 8 medium, 4 hard, 3 very hard, 1 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Both. In the bank, Paper 1: 17 · Paper 2: 8. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.
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.