Exercises for Question Type 6: Finding missing values in a box and whisker plot using given information

Question 1

Skill question

For a data set, the five-number summary is given by: $min = 3, Q_{1}, median, Q_{3} = 21, max = 33$ .

Given that $Q_{1} + Q_{3} = 30$ and the median is the average of $Q_{1}$ and $Q_{3}$ , find the value of $Q_{1}$ and the median.

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Question 2

Skill question

In a box and whisker plot, $Q_{1} = 7$ and the distance from $Q_{1}$ to the median is 5. The distance from the median to $Q_{3}$ is twice the distance from $Q_{1}$ to the median. Find the median and $Q_{3}$ .

[3]

Question 3

Skill question

In a box and whisker plot, the five-number summary is $min = - 2$ , $Q_{1} = 5$ , $median = 12$ , $Q_{3} = 20$ , and $max$ is missing. The interquartile range equals half the total range. Find the missing value of $max$ .

[3]

Question 4

Skill question

A symmetric box and whisker plot has $min = 2$ , $max = 18$ , and $median = 10$ . The interquartile range is 8.

Find the value of $Q_{1}$ and $Q_{3}$ .

[4]

Question 5

Skill question

For a box plot, the five-number summary is $min = 4$ , $Q_{1} = 8$ , median missing, $Q_{3}$ missing, and $max = 28$ . The box (from $Q_{1}$ to $Q_{3}$ ) spans one quarter of the total range and is centered around the median. Find the median and $Q_{3}$ .

[4]

Question 6

Skill question

This question assesses the ability to use the five-number summary and interquartile range (IQR) to find a missing quartile value in a box-and-whisker plot.

In a box-and-whisker plot, the five-number summary is given by: $min = 4$ , $Q_{1} = 10$ , $median = 13$ , $Q_{3}$ is missing, and $max = 25$ .

Given that the interquartile range (IQR) is 12, find the value of $Q_{3}$ .

[2]

Question 7

Skill question

A box plot gives $min = 10$ , $Q_{1} = 18$ , $median = 26$ , $Q_{3}$ missing, and $max$ missing. The interquartile range is 16 and the total range is 30. Find $Q_{3}$ and $max$ .

[4]

Question 8

Skill question

A box and whisker plot has $min = 2$ , $Q_{1} = 8$ , $median$ missing, $Q_{3} = 18$ , $max = 26$ . The median is exactly halfway between $Q_{1}$ and $Q_{3}$ . Find the median. [2 marks]

[2]

Question 9

Skill question

A data set has a minimum value of $2$ and a maximum value of $22$ . Two points, $P_{1}$ and $P_{2}$ , divide the total range into three equal parts such that $P_{1}$ is one-third of the way from the minimum to the maximum and $P_{2}$ is two-thirds of the way from the minimum to the maximum.

Find the values of $P_{1}$ and $P_{2}$ .

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Question 10

Skill question

In a data set, the five-number summary is $min = 0$ , $Q_{1}$ missing, $median = 24$ , $Q_{3}$ missing, and $max = 48$ . The quartiles $Q_{1}$ and $Q_{3}$ split the total range into equal thirds. Find the values of $Q_{1}$ and $Q_{3}$ .

[3]

Question 11

Skill question

Calculations involving the five-number summary and interquartile distances.

In a data set, the five-number summary is $min = 6$ , $Q_{1}$ is missing, $median = 14$ , $Q_{3} = 20$ , and $max = 30$ . The distance from the median to $Q_{3}$ is $4$ units greater than the distance from $Q_{1}$ to the median. Find $Q_{1}$ .

[3]

Question 12

Skill question

In a box plot, $min = 4$ , $median = 10$ , and the values for $Q_{1}, Q_{3}$ , and $max$ are missing. The distance from the median to $Q_{3}$ is twice the distance from $Q_{1}$ to the median, the interquartile range is 6, and the total range is 12.

Find $Q_{1}, Q_{3}$ , and $max$ .

[5]

IB Mathematics Applications & Interpretation Question Type 6: Finding Missing Values in a Box and Whisker Plot Using Given Information Exercises