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Statistics & Probability - IB Questionbank | RevisionDojo

Practice Statistics & Probability with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

Here are the heights, in cm, of $7$ plants:

$25, 22, 28, 20, 26, 21, 23$

Find the median height.

[1]

A sack contains $8$ potatoes. The mean mass of the potatoes is $120$ g. One potato is removed from the sack. The mean mass of the remaining $7$ potatoes is $115$ g. Work out the mass of the potato that was removed.

[2]

Question 2

SL & HLPaper 1

A small group of students recorded the number of hours they spent studying for a test: $2, 3, 5, 2, 4, 3, 2$ .

Find the mean number of hours.

[1]

Find the median number of hours.

[1]

Find the mode number of hours.

[1]

Question 3

SL & HLPaper 1

A student took three quizzes. Her mean score was $7$ . Her median score was $6$ . Her highest score was $8$ marks more than her lowest score.

Find the number of marks she scored in each of the three quizzes.

[3]

The student took a fourth quiz. The mean of her four scores was $9$ marks. Find the number of marks that the student scored in the fourth quiz.

[3]

Question 4

SL & HLPaper 1

The heights (in cm) of 50 plants are recorded in the following frequency table:

Height $(\mathrm{cm})$	Frequency
$20 \leq h<30$	10
$30 \leq h<40$	15
$40 \leq h<50$	12
$50 \leq h<60$	8
$60 \leq h<70$	5

Estimate the mean height of the plants.

[3]

Determine the modal class.

[1]

Estimate the probability that a randomly selected plant has a height of at least 50 cm.

[2]

Question 5

SL & HLPaper 1

The scores, $x$ , obtained by $15$ students in a Mathematics quiz are shown below. $32, 45, 28, 39, 41, 35, 25, 48, 30, 42, 38, 36, 40, 33, 44$

Find the median score.

[2]

Find the lower quartile and the upper quartile of the scores.

[4]

Calculate the interquartile range of the scores.

[1]

Question 6

SL & HLPaper 1

The scores of $25$ students on a short mathematics quiz are summarized in the frequency table below:

Score (x)	0	1	2	3	4	5
Frequency (f)	2	4	7	6	4	2

Find the lower quartile ( $Q_1$ ) of the scores.

[2]

Find the upper quartile ( $Q_3$ ) of the scores.

[2]

Calculate the interquartile range (IQR).

[2]

Question 7

SL & HLPaper 1

The number of customers served by a shop assistant each hour over a $10$ -hour period is shown below:

$8, 12, 10, 9, 15, 11, 8, 10, 12, 9$

Find the median number of customers served.

[2]

Calculate the mean number of customers served.

[2]

Suppose the largest value, $15$ , was mistakenly recorded as $25$ . Explain how this correction would affect the mean and median calculated in parts (a) and (b).

[4]

Question 8

SL & HLPaper 1

A librarian records the number of books borrowed, $B$ , and the number of library visits, $V$ , by eight members over a month. The data are shown below.

Books borrowed $(B)$	Library visits $(V)$
2	1
4	2
6	3
8	4
10	5
12	6
14	7
16	8

Find Pearson's product-moment correlation coefficient, $r$ , and interpret its value in context.

[3]

Find the equation of the regression line $V$ on $B$ .

[2]

Estimate the number of library visits for a member who borrows 9 books.

[2]

Draw a scatter diagram of the data with the regression line.

[3]

Question 9

SL & HLPaper 1

A bag contains 12 cards labeled with the numbers 1 to 12 . Three cards are drawn randomly without replacement.

Find the probability that the first card drawn is even-numbered.

[1]

Find the probability that the second card drawn is odd-numbered given that the first card was even-numbered.

[2]

Find the probability that all three cards drawn are even-numbered.

[3]

Question 10

SL & HLPaper 1

Consider four integers $a$ , $b$ , $c$ , and $d$ such that $a<b<c<d$ .

Let $a<b<c<d$ where the maximum is twice the range, and the median is 10. Find the value of $a$ for which the mean is 11.

[4]

Let $a$ and $d$ be the same as your answers to part (a), but $b$ and $c$ have been altered. If $a,b,c,d$ create a geometric sequence, find the median.

[4]

Statistics & Probability Questionbank