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Question 1
A dataset of daily temperatures (°C) recorded over 30 days is displayed in a box plot. The box spans from 14°C to 22°C, the median line is at 16°C, the left whisker ends at 8°C, and the right whisker ends at 29°C. What is the interquartile range (IQR) of this dataset?
No clue? Show me the answer
Correct answerCorrect!Incorrect
A8°C
Step-by-step walkthrough
Choose a solution method
Method #1Approach 1
Step 1: Identify the quartiles from the box plot
In a box plot, the left edge of the box is $Q_{1}$ and the right edge of the box is $Q_{3}$ . Here, $Q_{1} = 14$ °C and $Q_{3} = 22$ °C.
Step 2: Apply the IQR formula
The interquartile range is calculated as: $IQR = Q_{3} - Q_{1} = 22 - 14 = 8 °C$
Step 3: Select the correct answer
The IQR is 8°C. Note that the whiskers represent the minimum and maximum values, not the quartiles — these must not be used in the IQR calculation.
Method #2Approach 2
Step 1: Identify what is being asked
The question asks for the IQR, which is the length of the box (from $Q_{1}$ to $Q_{3}$ ), not the full range of the data.
Step 2: Eliminate 21°C
21°C would be the full range ( $29 - 8 = 21$ ). This is the range, not the IQR — eliminate it.
Step 3: Eliminate 6°C
6°C might come from subtracting the median from $Q_{3}$ : $22 - 16 = 6$ . This is not the IQR formula — eliminate it.
Step 4: Eliminate 14°C
14°C is the value of $Q_{1}$ itself, not the IQR — eliminate it.
Step 5: Select the correct answer
$Q_{3} - Q_{1} = 22 - 14 =$ 8°C is the only value consistent with the correct IQR formula.
Question 2
The masses (in kg) of parcels handled by a delivery service are recorded in the following frequency table:

Mass $m$ (kg) Frequency
$0 \leq m < 2$ 5
$2 \leq m < 4$ 14
$4 \leq m < 6$ 20
$6 \leq m < 8$ 9
$8 \leq m < 10$ 2

What is the modal class for this data?
No clue? Show me the answer
Correct answerCorrect!Incorrect
A $4 \leq m < 6$
Step-by-step walkthrough
Choose a solution method
Method #1Approach 1
Step 1: Identify what the modal class is
The modal class is the class interval with the highest frequency in a grouped frequency distribution.
Step 2: Find the highest frequency
Scanning the frequency column: 5, 14, 20, 9, 2. The highest frequency is 20, which belongs to the class $4 \leq m < 6$ .
Step 3: State the modal class
The modal class is $4 \leq m < 6$ . We say modal class rather than mode because the data is grouped and individual values are unknown.
Method #2Approach 2
Step 1: Identify what is being asked
The question asks for the modal class — the interval with the greatest frequency.
Step 2: Eliminate $0 \leq m < 2$
$0 \leq m < 2$ has frequency 5, which is the lowest — eliminate it.
Step 3: Eliminate $2 \leq m < 4$
$2 \leq m < 4$ has frequency 14, which is high but not the highest — eliminate it.
Step 4: Eliminate $6 \leq m < 8$
$6 \leq m < 8$ has frequency 9, less than 20 — eliminate it.
Step 5: Select the correct answer
$4 \leq m < 6$ has the highest frequency of 20, making it the modal class.

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13 more questions in this topic

Mass

m

(kg)

Frequency

0 \leq m < 2

2 \leq m < 4

4 \leq m < 6

6 \leq m < 8

8 \leq m < 10

SL 4.2—Histograms, CF graphs, box plots

Step-by-step walkthrough

Step 1: Identify the quartiles from the box plot

Step 2: Apply the IQR formula

Step 3: Select the correct answer

Step 1: Identify what is being asked

Step 2: Eliminate 21°C

Step 3: Eliminate 6°C

Step 4: Eliminate 14°C

Step 5: Select the correct answer

Step-by-step walkthrough

Step 1: Identify what the modal class is

Step 2: Find the highest frequency

Step 3: State the modal class

Step 1: Identify what is being asked

Step 2: Eliminate $0 \leq m < 2$

Step 3: Eliminate $2 \leq m < 4$

Step 4: Eliminate $6 \leq m < 8$

Step 5: Select the correct answer

13 more questions in this topic

SL 4.2—Histograms, CF graphs, box plots

Step-by-step walkthrough

Step 1: Identify the quartiles from the box plot

Step 2: Apply the IQR formula

Step 3: Select the correct answer

Step 1: Identify what is being asked

Step 2: Eliminate 21°C

Step 3: Eliminate 6°C

Step 4: Eliminate 14°C

Step 5: Select the correct answer

Step-by-step walkthrough

Step 1: Identify what the modal class is

Step 2: Find the highest frequency

Step 3: State the modal class

Step 1: Identify what is being asked

Step 2: Eliminate $0 \leq m < 2$

Step 3: Eliminate $2 \leq m < 4$

Step 4: Eliminate $6 \leq m < 8$

Step 5: Select the correct answer

13 more questions in this topic

Mass $m$ (kg)	Frequency
$0 \leq m < 2$	5
$2 \leq m < 4$	14
$4 \leq m < 6$	20
$6 \leq m < 8$	9
$8 \leq m < 10$	2