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

Question 1

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

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.

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Question 3

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.

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Question 4

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

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

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Question 6

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?

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Question 7

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} .

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Question 8

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]

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Question 9

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.

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Question 10

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 .

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Question 11

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.

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Question 12

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.

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