Exercises for Question Type 4: Interpretating information from box and whisker plots

Question 1

Skill question

Two boxplots represent the heights of plants under Treatment A and Treatment B.

Treatment A: $Q_{1} = 15$ , median $= 20$ , $Q_{3} = 25$ . Treatment B: $Q_{1} = 18$ , median $= 22$ , $Q_{3} = 24$ .

Determine which treatment shows less variability. Justify your answer.

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Question 2

Skill question

For a set of daily sales, the summary statistics are $min = 50$ , $Q_{1} = 75$ , $median = 100$ , and $Q_{3} = 150$ . The maximum value in the dataset is recorded as $350$ .

Use the $1.5 \times IQR$ rule to determine if the value of $350$ is an outlier.

[4]

Question 3

Skill question

The question tests the ability to identify the median from a summary of a boxplot's key values.

A boxplot shows the first quartile at $15$ , the median at $30$ , and the third quartile at $45$ .

State the median value of the dataset.

[1]

Question 4

Skill question

For a dataset with the following five-number summary: $min = 3$ , $Q_{1} = 9$ , $median = 12$ , $Q_{3} = 18$ , and $max = 35$ , determine whether the value $35$ is an outlier using the $1.5 \times I QR$ rule.

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Question 5

Skill question

Given the five-number summary: $min = 4, Q_{1} = 8, median = 12, Q_{3} = 16, max = 28$ , describe the skewness of the data distribution.

[3]

Question 6

Skill question

A dataset of 200 values has five-number summary: $min = 2, Q_{1} = 5, median = 7, Q_{3} = 10, max = 20$ . Approximately how many values are below the median?

[2]

Question 7

Skill question

In a boxplot, $Q_{1} = 10$ , $median = 12$ , and $Q_{3} = 14$ . Determine the percentage of the data that lies between $Q_{1}$ and $Q_{3}$ .

[2]

Question 8

Skill question

The five-number summary of a dataset is: minimum $= 10$ , $Q_{1} = 20$ , median $= 35$ , $Q_{3} = 50$ , maximum $= 70$ .

Calculate the interquartile range. [2 marks]

[2]

Question 9

Skill question

A dataset has a five-number summary: minimum = $12$ , $Q_{1} = 25$ , median = $40$ , $Q_{3} = 55$ , maximum = $80$ . Determine the range of the dataset.

[2]

Question 10

Skill question

A boxplot of exam scores shows the median is closer to $Q_{1}$ than to $Q_{3}$ , and the upper whisker is longer than the lower whisker. Is the distribution skewed left or right? Explain.

[3]

Question 11

Skill question

Dataset A has the five-number summary: $min = 5$ , $Q_{1} = 15$ , $median = 25$ , $Q_{3} = 35$ , $max = 45$ . Dataset B has the five-number summary: $min = 0$ , $Q_{1} = 10$ , $median = 20$ , $Q_{3} = 40$ , $max = 50$ .

Determine which dataset has greater variability. Justify your answer using the interquartile range.

[4]

Question 12

Skill question

A box and whisker plot has whiskers at $8$ and $62$ , and the box spans from $20$ to $50$ . Calculate the lengths of the lower and upper whiskers.

[2]

IB Mathematics Applications & Interpretation Question Type 4: Interpretating Information from Box and Whisker Plots Exercises