IB Maths AI SL · Unit 4: Statistics and Probability
IB Maths AI SL Bivariate Data Questions
Exam-style IB Maths AI SL bivariate 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.
- 30 questions
- Paper 1: 17
- Paper 2: 13
- 3 easy
- 9 medium
- 8 hard
- 5 very hard
- 5 starter
- 3 worked examples
Practise Bivariate Data questions →
AI SL formula booklet
What's examined in AI SL bivariate data
The question bank covers these bivariate data question types (number of questions in brackets):
- Linear Regression (15)
- Correlation Analysis (10)
- Scatter Plots & Modelling (5)
Key formulas
- Mean of a data set
- \(\bar{x} = \dfrac{\sum_{i=1}^{n} f_i x_i}{n}, \quad n = \sum f_i\)
In the same notation as the IB formula booklet. All AI SL formulas →
Bivariate Data worked examples
Worked example 1: Pearson's correlation coefficient · easy
A researcher records hours of sunshine $x$ and ice creams sold $y$ over $5$ days: $(2,12), (4,20), (6,26), (8,36), (10,46)$. Find $r$ to 3 s.f. and interpret it.
1. Enter: $x$-values in List 1, $y$-values in List 2 on the GDC.
2. Run: 2-Var linear regression (LinReg $ax+b$).
3. Extract: $r = 0.993399\ldots$
4. State: $\mathbf{r = 0.993}$.
5. Interpret: Very strong, positive linear correlation between sunshine and sales.
Examiner tip: If your GDC doesn't display $r$, enable "Diagnostics" in the catalogue or mode settings.
Worked example 2: Regression line and prediction · medium
Using the same data, find the regression line $y=ax+b$, then estimate ice creams sold with $7$ hours of sunshine.
1. Run: LinReg on the GDC using the same lists.
2. Extract: $a=4.2$, $b=2.8$.
3. Equation: $\mathbf{y = 4.2x + 2.8}$.
4. Substitute: $y = 4.2(7) + 2.8 = 32.2$.
5. State: approximately $\mathbf{32}$ ice creams.
Examiner tip: Always use the regression line of $y$ on $x$ when predicting a $y$-value from an $x$-value.
Worked example 3: Reliability and extrapolation · hard
The kiosk owner uses $y=4.2x+2.8$ to predict $103.6$ sales for $x=24$ hours. Explain mathematically why this is unreliable.
1. Original domain: $2 \le x \le 10$.
2. Compare: $x = 24$ lies far outside this range.
3. Classify: This is extrapolation.
4. State: The estimate is unreliable — no guarantee the linear trend holds beyond $10$ hours.
Examiner tip: Even with $r=1.00$, any prediction outside the poles of the data must be classified as unreliable.
Try these IB Maths AI SL bivariate data questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Question 1 · easy · 4 marks · Paper 1
A set of bivariate data has a regression line \(y\) on \(x\) with the equation \(y = 3.5x + 12\). The mean value of the \(x\)-data is \(\overline{x} = 8\).
State the exact coordinates of the mean point, \(M(\overline{x}, \overline{y})\), for this data set.
Explain the mathematical significance of the mean point in relation to the line of best fit.
Question 2 · medium · 4 marks · Paper 1
A student investigates the relationship between the shoe size of primary school children and their reading speed in words per minute. The student calculates a Pearson’s correlation coefficient of \(r = 0.89\).
State the direction and strength of the linear correlation.
The student concludes that having larger feet causes children to read faster. Explain why this conclusion is invalid, suggesting a possible lurking variable.
Question 3 · hard · 4 marks · Paper 1
The weights of 10 athletes and the weights of their corresponding bicycles are recorded. The Pearson’s correlation coefficient is found to be \(r = 0.76\). The researcher realises that the bicycle weights were recorded in kilograms, but they should have been recorded in grams (by multiplying every bicycle weight by 1000).
State the new value of \(r\) after the bicycle weights are converted to grams.
Give a mathematical reason for your answer to part (a).
All 30 bivariate data questions with mark schemes →
FAQ
How many IB Maths AI SL bivariate data questions are there?
There are 30 exam-style bivariate data questions in the AI SL question bank (Paper 1: 17 · Paper 2: 13), graded 3 easy, 9 medium, 8 hard, 5 very hard, 5 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is bivariate data on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 17 · Paper 2: 13. 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.
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