IB Maths AA SL · Unit 4: Statistics and Probability
IB Maths AA SL Bivariate Data and Correlation Questions
Exam-style IB Maths AA SL bivariate data and correlation 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.
- 31 questions
- Paper 1: 9
- Paper 2: 22
- 8 easy
- 13 medium
- 5 hard
- 3 very hard
- 2 starter
- 3 worked examples
Practise Bivariate Data and Correlation questions →
AA SL formula booklet
What's examined in AA SL bivariate data and correlation
The question bank covers these bivariate data and correlation question types (number of questions in brackets):
- Linear Regression Equation (22)
- Pearson's Correlation Coefficient (5)
- Regression Line Properties (4)
Key formulas
- Mean of a data set
- \(\bar{x} = \dfrac{\sum f_i x_i}{n},\ n = \sum f_i\)
In the same notation as the IB formula booklet. All AA SL formulas →
Bivariate Data and Correlation worked examples
Worked example 1: Finding linear regression parameters · easy
Primary school children's ages $x$ and mean weights $y$ kg: $(6.25, 21.5), (7.35, 23.1), (8.50, 26.9), (9.25, 28.6), (10.75, 32.0)$. The relationship is modelled by $y = ax + b$. Find $a$, $b$ and Pearson's $r$.
1. Access the GDC Statistics menu.
2. Input ages into List 1 and weights into List 2.
3. Execute linear regression (CALC $\to$ REG $\to$ X $\to$ ax+b).
4. Read the coefficients: $a = 2.4563\ldots$, $b = 5.7533\ldots$
5. State to 3 s.f.: $\mathbf{a = 2.46}$, $\mathbf{b = 5.75}$.
6. Correlation coefficient: $\mathbf{r = 0.989}$.
Examiner tip: Ensure "Diagnostics On" is enabled so $r$ appears alongside $a$ and $b$.
Worked example 2: Predicting values and reliability · medium
Regression line $y = 5.30x + 34.9$ where the sample $x$ ranged $5.9$ to $9.4$ hours. Estimate the score for $x = 10.5$ hours and comment on reliability.
1. Substitute: $y = 5.30(10.5) + 34.9 = 55.65 + 34.9$.
2. Evaluate: $y = 90.55 \implies \mathbf{90.6}$.
3. Analyse the sample range: $10.5 > 9.4$ (outside the observed range).
4. Conclude: the estimate is unreliable because it involves extrapolation.
Examiner tip: High $r$ does NOT rescue extrapolated predictions. Any $x$ outside the observed range makes the estimate unreliable.
Worked example 3: Reversing the regression lines · hard
Regression line $P$ on $D$: $P = 0.088D + 13.9$; regression line $D$ on $P$: $D = 6.22P + 116$. A customer has budget $P = \text{€}100$. Predict the maximum distance.
1. Identify: we know $P$, we want $D$. Use the line of $D$ on $P$.
2. Equation: $D = 6.22P + 116$.
3. Substitute: $D = 6.22(100) + 116 = 622 + 116$.
4. State: $\mathbf{D = 738}$ km.
Examiner tip: Never rearrange the "$P$ on $D$" line algebraically to predict $D$. Regression lines minimise vertical errors in one direction only.
Try these IB Maths AA SL bivariate data and correlation 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 · 3 marks · Paper 2
The regression line of $y$ on $x$ for a bivariate dataset is given by $y = -2.5x + 10.4$. The mean of the $x$-values in the dataset is $3.2$. Find the exact mean of the $y$-values.
Question 2 · medium · 4 marks · Paper 1
The equation of a regression line linking the number of hours a student spends studying for a math exam (\(x\)) and their final score out of 100 (\(y\)) is given by \(y = 5.2x + 34.5\).
Interpret the meaning of the parameter \(5.2\) in the context of the question.
Interpret the meaning of the parameter \(34.5\) in the context of the question.
A student concludes that "studying for exactly 10 hours causes your score to increase by 52 marks." Explain why this statement is statistically flawed.
Question 3 · hard · 5 marks · Paper 1
For a dataset containing \(n = 10\) pairs of bivariate data \((x, y)\), the equation of the regression line of \(y\) on \(x\) is given by \(y = 3.2x - 14.5\).
Given that the sum of all the \(x\)-values is \(\sum x = 60\):
Find the mean of \(x\), \(\bar{x}\).
Use the properties of the regression line to find \(\bar{y}\).
Hence, find the exact sum of all the \(y\)-values, \(\sum y\).
All 31 bivariate data and correlation questions with mark schemes →
FAQ
How many IB Maths AA SL bivariate data and correlation questions are there?
There are 31 exam-style bivariate data and correlation questions in the AA SL question bank (Paper 1: 9 · Paper 2: 22), graded 8 easy, 13 medium, 5 hard, 3 very hard, 2 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is bivariate data and correlation on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 9 · Paper 2: 22. 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.
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