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IB Maths AI SL · Unit 4: Statistics and Probability

IB Maths AI SL Descriptive Statistics Questions

Exam-style IB Maths AI SL descriptive statistics 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.

Practise Descriptive Statistics questions → AI SL formula booklet

What's examined in AI SL descriptive statistics

The question bank covers these descriptive statistics question types (number of questions in brackets):

Key formulas

Interquartile range
\(\mathrm{IQR} = Q_3 - Q_1\)
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 →

Descriptive Statistics worked examples

Worked example 1: Mean, median, and mode · easy

Goals scored in seven matches: $4, 6, 6, 8, 11, 12, 16$. Write down the mode and median, and calculate the exact mean.

Solution

1. Mode: most frequent value $= \mathbf{6}$.

2. Median: 4th of 7 sorted values $= \mathbf{8}$.

3. Mean formula: $\bar{x} = \frac{\sum x}{n}$.

4. Substitute: $\bar{x} = \frac{4+6+6+8+11+12+16}{7} = \frac{63}{7}$.

5. Evaluate: $\mathbf{\bar{x} = 9}$.

Examiner tip: With an even number of values, the median is the mean of the two middle numbers. Always sort first!

Worked example 2: Testing for outliers · medium

Weights: $Q_1=135\text{ g}$, median $=190\text{ g}$, $Q_3=242\text{ g}$, max $=390\text{ g}$. Is $390$ an outlier?

Solution

1. IQR: $Q_3 - Q_1 = 242 - 135 = 107\text{ g}$.

2. Upper boundary: $Q_3 + 1.5 \times \text{IQR} = 242 + 1.5(107)$.

3. Evaluate: $242 + 160.5 = 402.5\text{ g}$.

4. Compare: $390 < 402.5$.

5. Conclude: $390\text{ g}$ is not an outlier.

Examiner tip: The lower boundary is $Q_1 - 1.5 \times \text{IQR}$. Memorise both — they are not in the formula booklet.

Worked example 3: Mean from grouped frequency data · hard

$60$ commuter distances: $[0,10)$: 4, $[10,20)$: 11, $[20,30)$: 25, $[30,40)$: 16, $[40,50)$: 4. Estimate the mean to 3 s.f.

Solution

1. Midpoints: $5, 15, 25, 35, 45$.

2. Enter: midpoints in List 1, frequencies in List 2 on GDC.

3. Set: 1-Var Stats with List 2 as frequency.

4. Or compute: $\frac{4(5)+11(15)+25(25)+16(35)+4(45)}{60} = \frac{1550}{60}$.

5. Evaluate: $25.833\ldots \Rightarrow \mathbf{25.8\text{ km}}$.

Examiner tip: It is an "estimate" because we assume every commuter travelled exactly the mid-interval distance.

Try these IB Maths AI SL descriptive statistics 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 · 6 marks · Paper 1

The daily wait times, in minutes, for a bus are recorded over 8 days: \[5, \ 12, \ 14, \ 15, \ 18, \ 21, \ 24, \ 45\]

  1. Find the lower quartile (\(Q_1\)) and the upper quartile (\(Q_3\)) of the wait times.

  2. Calculate the interquartile range (IQR).

  3. Determine if the wait time of \(45\) minutes is considered an outlier. Show all your working.

Attempt it and see the mark scheme →

Question 2 · medium · 6 marks · Paper 2

The mean of five distinct positive integers is \(8.4\).

  1. Find the sum of these five integers.

  2. A sixth integer, \(x\), is added to the data set. The new mean of all six integers is exactly \(9\). Find the value of \(x\).

  3. Two different classes took a mathematics test. Class A has 20 students and achieved a mean score of 65 marks. Class B has 30 students and achieved a mean score of 80 marks. Calculate the combined mean score for all 50 students.

Attempt it and see the mark scheme →

Question 3 · hard · 6 marks · Paper 1

The five numbers in a dataset, arranged in ascending order, are: \[x, \ \ x + 2, \ \ 2x - 3, \ \ 2x + 1, \ \ 3x - 4\] The median of this dataset is \(11\).

  1. Find the value of \(x\).

  2. Hence, list the five numbers in the dataset.

  3. Calculate the mean of the dataset.

Attempt it and see the mark scheme →

All 28 descriptive statistics questions with mark schemes →

FAQ

How many IB Maths AI SL descriptive statistics questions are there?

There are 28 exam-style descriptive statistics questions in the AI SL question bank (Paper 1: 19 · Paper 2: 9), graded 3 easy, 14 medium, 4 hard, 5 very hard, 2 starter. Every question has a full IB-style mark scheme (M, A and R marks).

Is descriptive statistics on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 19 · Paper 2: 9. 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.

More AI SL Unit 4 topics

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