SL 4.1—Concepts, reliability and sampling techniques Questionbank

Practice SL 4.1—Concepts, reliability and sampling techniques 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 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 3

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 4

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 5

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 recorded incorrectly and the correct value is $25$ . Explain how this correction would affect the mean and median calculated in parts 1 and 2.

[4]

Question 6

SL & HLPaper 1

Consider four real numbers $a$ , $b$ , $c$ , 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 $a$ be the value found in part 1, and $d$ be the corresponding maximum value. If $a, b, c, d$ form a geometric sequence, find the median.

[4]

Question 7

SLPaper 1

Consider three integers $a$ , $b$ , $c$ which form a strictly increasing arithmetic sequence in that order.

Show that $b$ is the mean of $a$ and $c$ .

[2]

If $2b$ is the range, find the value of $a$ .

[2]

A student said that this forms a geometric sequence of common ratio 2. Is that correct? Explain why or why not.

[2]

Question 8

SL & HLPaper 1

A group of four numbers has a mean of $7$ , a median of $6$ and a mode of $6$ . The numbers $4$ and $10$ are added to the group.

Find the mean of the six numbers.

[2]

Find the median of the six numbers.

[2]

Question 9

SL & HLPaper 1

A meteorological station recorded the deviation from the average temperature, in $^\circ\text{C}$ , at 10 different times during a day. The results are given below: $-5, -3, -1, 0, 1, 2, 3, 3, 4, -4$

For these results, find the median.

[2]

For these results, find the mean.

[2]

Later, two additional readings were recorded. When these two new readings were included, the new mean for all 12 readings became $0.5^\circ\text{C}$ , and the new median became $1^\circ\text{C}$ . Find the two new readings.

[4]

Question 10

SLPaper 1

Consider the following data sets $X$ and $Y$ such that $X=\{x-4, \, x, \, 2x, \, x+9\}$ and $Y=\{y, \, 2y, \, 3y-6\}$ .

Find the mean of $X$ and $Y$ in terms of $x$ and $y$ respectively.

[2]

State what happens to the mean and variance if all the values increase by a constant $k$ .

[2]

Given the means of $X$ and $Y$ are equal and that $x$ and $y$ are also equal, find the actual values of the means.

[3]

Score (x)

Frequency (f)