IB Maths AI HL · Unit 4: Statistics and Probability
IB Maths AI HL Data Collection and Non-Linear Regression Questions
Exam-style IB Maths AI HL data collection and non-linear regression 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.
- 17 questions
- Paper 1: 17
- 5 easy
- 4 medium
- 5 hard
- 3 starter
- 3 worked examples
Practise Data Collection and Non-Linear Regression questions →
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What's examined in AI HL data collection and non-linear regression
The question bank covers these data collection and non-linear regression question types (number of questions in brackets):
- Non-linear Model Evaluation (11)
- Data Collection Principles (5)
- Data Transformation for Linearization (1)
Data Collection and Non-Linear Regression worked examples
Worked example 1: Distinguishing Reliability and Validity · easy
A psychology student uses a faulty ruler that has shrunk in the sun to measure the length of $20$ wooden blocks. The student measures each block three times, getting almost identical results each time, but all measurements are fundamentally shorter than the true lengths. Determine whether this data collection method is reliable and whether it is valid, giving a reason for each.
1. Recall that 'reliable' means the measurements are consistent and repeatable.
2. Conclude on reliability: The method is reliable because repeating the measurement yields almost identical results.
3. Recall that 'valid' means the measurement tool accurately measures what it is supposed to measure (the true value).
4. Conclude on validity: The method is not valid because the faulty ruler introduces a systematic error, meaning it does not measure the true length of the blocks.
Examiner tip: In IB terminology, reliability is synonymous with precision (low variance), while validity is synonymous with accuracy (low bias/systematic error).
Worked example 2: Performing Exponential Regression · medium
The population of a bacteria colony, $P$, is recorded over $t$ hours. The data points $(t, P)$ are: $(1, 15)$, $(2, 44)$, $(3, 133)$, $(4, 405)$. Use your Graphic Display Calculator to find the equation of the exponential regression curve in the form $P(t) = a \cdot b^t$.
1. Enter the data into the GDC statistics lists: List 1 (Time, $t$) and List 2 (Population, $P$).
2. Navigate to the calculation menu and select exponential regression (ExpReg or $ab^x$).
3. Ensure List 1 is set to $X$ and List 2 is set to $Y$.
4. Execute the regression and extract the parameters: $a = 4.881\dots$ and $b = 3.010\dots$
5. Write the final equation rounded to 3 significant figures: $P(t) = 4.88 \times 3.01^t$.
Examiner tip: Pay close attention to the requested form of the exponential equation. Some questions ask for $y = a \cdot e^{kx}$ while others ask for $y = a \cdot b^x$. Use the correct regression tool on your GDC accordingly.
Worked example 3: Making Predictions and Evaluating Extrapolation · hard
Using the regression model $P(t) = 4.88 \times 3.01^t$ from the previous example, estimate the bacteria population at $t = 12$ hours. State whether this estimate is reliable and justify your answer.
1. Substitute $t = 12$ into the exponential model: $P(12) = 4.88 \times 3.01^{12}$.
2. Evaluate using the GDC: $P(12) \approx 2\,666\,285$.
3. State the estimate: The estimated population is $2\,670\,000$ bacteria (to 3 s.f.).
4. Analyse the reliability based on the original data range ($t=1$ to $t=4$).
5. Conclude: The estimate is not reliable.
6. Justify: It relies heavily on extrapolation far outside the known data range, and exponential growth models rarely continue indefinitely in reality due to limiting factors like space and resources.
Examiner tip: Estimates made via extrapolation are inherently unreliable. Even if a model has an $R^2$ value of $1.00$ inside the data range, you must state that extrapolating outside the domain renders the prediction untrustworthy.
Try these IB Maths AI HL data collection and non-linear regression 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 researcher wishes to survey the students in a high school. The school has 200 freshmen, 300 sophomores, 400 juniors, and 100 seniors. The researcher selects exactly 20 freshmen, 30 sophomores, 40 juniors, and 10 seniors at random.
Name the specific sampling method used, and state one advantage of this method over simple random sampling.
Question 2 · medium · 6 marks · Paper 1
A survey asks the question: "Given the recent horrific increase in violent crime, do you support the mayor’s new highly effective policing policy?"
Identify two distinct types of bias present in the wording of this question, and rewrite the question to make it valid and unbiased.
Question 3 · hard · 8 marks · Paper 1
A dataset measuring the stopping distance of a car \(D\) (metres) against its speed \(v\) (km/h) is modelled by two different equations:
Model A (Quadratic): \(D_A = 0.006v^2 + 0.2v\)
Model B (Exponential): \(D_B = 2.5 \times 1.04^v\)
At \(v = 100\) km/h, the actual measured stopping distance is \(82\) metres.
Calculate the residual at \(v=100\) for both models. State which model provides the most accurate prediction at this speed.
All 17 data collection and non-linear regression questions with mark schemes →
FAQ
How many IB Maths AI HL data collection and non-linear regression questions are there?
There are 17 exam-style data collection and non-linear regression questions in the AI HL question bank (Paper 1: 17), graded 5 easy, 4 medium, 5 hard, 3 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is data collection and non-linear regression on Paper 1 or Paper 2?
In the question bank these questions are set as Paper 1 questions.
Where can I get the mark schemes?
Open the AI HL 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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