IB Maths AA SL · Unit 4: Statistics and Probability
Exam-style IB Maths AA SL measures of central tendency 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.
SL AA rarely tests calculation — it tests INTERPRETATION. Which measure of centre is robust to outliers? Which measure of spread does the IB expect? Mean, median, mode, and IQR overview →
The question bank covers these measures of central tendency question types (number of questions in brackets):
Goals scored in 7 matches: $1, 3, 0, 2, 2, 5, 1$. Find mode, median, mean.
1. Modes: $1$ and $2$ each appear twice — bimodal: $\mathbf{1 \text{ and } 2}$.
2. Order: $0, 1, 1, 2, 2, 3, 5$.
3. Median (4th of 7): $\mathbf{2}$.
4. Sum: $14$; mean: $\frac{14}{7} = \mathbf{2}$.
Mean weight of 5 apples is $120$ g. A 6th apple joins; new mean is $125$ g. Find the weight of the 6th apple.
1. Original sum: $S_5 = 5 \times 120 = 600$ g.
2. Set up: $\frac{600 + x}{6} = 125$.
3. Multiply: $600 + x = 750$.
4. Solve: $x = \mathbf{150}$ g.
Group A: 20 students, mean 15, SD 3. Group B: 30 students, mean 20, SD 4. Find the combined group's SD.
1. Sums: $S_A = 300$, $S_B = 600$; combined mean $= 900/50 = 18$.
2. Sum of squares formula: $\sum x^2 = n(\sigma^2 + \mu^2)$.
3. Group A: $\sum x_A^2 = 20(9 + 225) = 4680$.
4. Group B: $\sum x_B^2 = 30(16 + 400) = 12480$.
5. Combined variance: $\frac{4680 + 12480}{50} - 18^2 = 343.2 - 324 = 19.2$.
6. Combined SD: $\sqrt{19.2} \approx \mathbf{4.38}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
A dataset of exam scores has a mean of \(42\) and a standard deviation of \(5\). The teacher decides to adjust the grades by multiplying every score by \(2\), and then adding \(10\) to each score. Find the exact value of:
the new mean.
the new standard deviation.
the new variance.
There are two mathematics classes, Class P and Class Q, who take the same examination. Class P has \(24\) students and a mean score of \(68\%\). Class Q has \(16\) students and a mean score of \(75\%\). Find the overall mean score of all \(40\) students combined. Give your answer to one decimal place.
A dataset consists of five discrete integers: \[-2, \quad 1, \quad a, \quad b, \quad 7\] The mode of the dataset is \(1\) and the mean is \(3\).
Deduce the values of \(a\) and \(b\).
Calculate the exact variance of the dataset.
All 20 measures of central tendency questions with mark schemes →
There are 20 exam-style measures of central tendency questions in the AA SL question bank (Paper 1: 13 · Paper 2: 7), graded 4 easy, 5 medium, 5 hard, 3 very hard, 3 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Both. In the bank, Paper 1: 13 · Paper 2: 7. 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.