Exercises for Question Type 4: Finding the value of the frequency of a specific class with some condition on mean, median or mode

Question 1

Skill question

The frequency table below shows the distribution of a continuous variable $x$ .

$Class 5 \leq x < 10 10 \leq x < 15 15 \leq x < 20 20 \leq x < 25 25 \leq x < 30 30 \leq x < 35 Frequency 58119 f 7$

Find the possible integer values of $f$ such that the mode lies in the class $25 \leq x < 30$ .

[4]

Question 2

Skill question

The following table shows the grouped frequency distribution for a set of data.

Class	Frequency
10–19	4
20–29	$f$
30–39	6
40–49	5
50–59	2

Find the value of $f$ , given that the mean of the distribution is 33.5.

[7]

Question 3

Skill question

Find the smallest integer value of $f$ such that the mode of the following grouped data is in the class 20–29.

$Class 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 Frequency 58 f 73$

[3]

Question 4

Skill question

The question asks for the unknown frequency $f$ in a grouped frequency distribution given the median of the distribution. Linear interpolation is used to solve for $f$ .

In the distribution below, find the value of $f$ such that the median of the distribution is 28.

Class	Frequency
10–19	4
20–29	$f$
30–39	6
40–49	4

[4]

Question 5

Skill question

The following question tests the ability to calculate a missing frequency from a grouped frequency distribution given the mean.

A grouped frequency distribution is shown in the table below. Given that the mean of the distribution is $60$ , find the value of $f$ .

Class	Frequency
$40 \le x < 50$	$3$
$50 \le x < 60$	$f$
$60 \le x < 70$	$4$
$70 \le x < 80$	$2$

[5]

Question 6

Skill question

Calculate the frequency $f$ so that the mean of the data values in the following table is 65.

Value	50	60	80
Frequency	2	$f$	3

[4]

Question 7

Skill question

The following table shows the frequency distribution for a set of discrete data, where $f$ represents the frequency of the class 16–20.

Find the minimum integer value of $f$ such that the modal class of this distribution is 16–20.

Class	Frequency
1–5	3
6–10	5
11–15	7
16–20	$f$
21–25	6

[3]

Question 8

Skill question

Determine the value of $f$ such that the median of the following frequency distribution is 45.

Class	Frequency
10–29	8
30–49	$f$
50–69	6
70–89	4

[5]

Question 9

Skill question

Given the grouped data below, find the minimum integer value of $f$ such that the modal class is $30 - 40$ .

$Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 4912 f 11$

[3]

Question 10

Skill question

A frequency distribution has classes 0–9, 10–19, 20–29, 30–39, 40–49 with frequencies $5$ , $f$ , $10$ , $8$ , $2$ . Find $f$ so that the mean of the distribution is $25$ .

[7]

Question 11

Skill question

The following table shows a frequency distribution.

Class	Frequency
$10\text{--}19$	$4$
$20\text{--}29$	$6$
$30\text{--}39$	$9$
$40\text{--}49$	$8$
$50\text{--}59$	$f$
$60\text{--}69$	$7$

Find the minimum integer value of $f$ such that the modal class is $50 - 59$ .

[3]

Question 12

Skill question

Questions involving finding an unknown frequency from a given mean for ungrouped discrete data.

The following ungrouped data have frequencies $1$ , $3$ , $f$ , $2$ and values $30$ , $40$ , $50$ , $60$ . Find $f$ so that the mean is $48$ .

[3]

IB Mathematics Applications & Interpretation Question Type 4: Finding the Value of the Frequency of a Specific Class with Some Condition on Mean, Median or Mode Exercises