IB Maths AA SL · Unit 4: Statistics and Probability
IB Maths AA SL Measures of Central Tendency Questions
Updated October 2026
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, showing the working that earns the marks — 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 →
What's examined in AA SL measures of central tendency
The question bank covers these measures of central tendency question types (number of questions in brackets):
Worked example 1: Basics of mean, median and mode · easy
Goals scored in 7 matches: . Find mode, median, mean.
Solution
1. Modes: and each appear twice — bimodal: .
2. Order: .
3. Median (4th of 7): .
4. Sum: ; mean: .
4 steps
Examiner tip: Always sort the data before locating the median — a shockingly common source of lost marks.
Worked example 2: Adjusting the mean with a new data point · medium
Mean weight of 5 apples is g. A 6th apple joins; new mean is g. Find the weight of the 6th apple.
Solution
1. Original sum: g.
2. Set up: .
3. Multiply: .
4. Solve: g.
4 steps
Examiner tip: Always revert to the SUM () when combining or updating means. Averages don't combine linearly.
Worked example 3: Combined variance of two datasets · hard
Group A: 20 students, mean 15, SD 3. Group B: 30 students, mean 20, SD 4. Find the combined group's SD.
Solution
1. Sums: , ; combined mean.
2. Sum of squares formula: .
3. Group A: .
4. Group B: .
5. Combined variance: .
6. Combined SD: .
5. Combined variance: .
6 steps · 1 to fill in
Examiner tip: You cannot average standard deviations directly. Rebuild the total sum-of-squares first, then re-apply the variance formula.
Try these IB Maths AA SL measures of central tendency 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
A dataset of exam scores has a mean of and a standard deviation of .
The teacher decides to adjust the grades by multiplying every score by , and then adding to each score.
Find the exact value of:
There are two mathematics classes, Class P and Class Q, who take the same examination.
Class P has students and a mean score of .
Class Q has students and a mean score of .
Find the overall mean score of all students combined. Give your answer to one decimal place.
Full worked solution Free, no sign-in
Total score for Class P . (M1)
Total score for Class Q . (M1)
Total combined score . (A1)
Total number of students .
Overall mean . A1
Every question here has a full worked solution.See them all →
Question 3 · hard · 5 marks · Paper 1
A dataset consists of five discrete integers:
The mode of the dataset is and the mean is .
How many IB Maths AA SL measures of central tendency questions are there?
There are 24 exam-style measures of central tendency questions in the AA SL question bank (Paper 1: 17 · Paper 2: 7), graded 6 easy, 9 medium, 6 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).
Is measures of central tendency on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 17 · Paper 2: 7. 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.