Sec 4 E-Math · Statistics

Box-and-whisker plots questions with answers

Practice questions on box-and-whisker plots, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the median.

Step 1 of 2

Read the five values: the whisker ends, the box ends and the line in the box

\text{min} = 12

Q_1 = 20

\text{median} = 26

Q_3 = 34

\text{max} = 46

Try a question: Box-and-whisker plots

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Questions

Question 1Read a box plot
The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the range.
Show the worked solution
1. Step 1: Read the five values: the whisker ends, the box ends and the line in the box $\text{min} = 22$ , $Q_1 = 30$ , $\text{median} = 34$ , $Q_3 = 42$ , $\text{max} = 48$
2. Step 2: Range = the whiskers' full length $\mathstrut \text{Range} = 48 - 22$ $\text{Range} = 26$
Question 2Read a box plot
The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the range.
Show the worked solution
1. Step 1: Read the five values: the whisker ends, the box ends and the line in the box $\text{min} = 14$ , $Q_1 = 22$ , $\text{median} = 28$ , $Q_3 = 36$ , $\text{max} = 42$
2. Step 2: Range = the whiskers' full length $\mathstrut \text{Range} = 42 - 14$ $\text{Range} = 28$
Question 3Compare two box plots
The box-and-whisker plots show the times, in minutes, taken by two groups, $A$ and $B$ . Find the difference between their medians.
Show the worked solution
1. Step 1: Read each plot $A$ : $\text{min} = 12$ , $Q_1 = 20$ , $\text{median} = 26$ , $Q_3 = 34$ , $\text{max} = 46$ $B$ : $\text{min} = 8$ , $Q_1 = 16$ , $\text{median} = 19$ , $Q_3 = 27$ , $\text{max} = 36$
2. Step 2: Subtract the medians $\mathstrut 26 - 19$ $\text{Difference} = 7$
Question 4Compare two box plots
The box-and-whisker plots show the times, in minutes, taken by two groups, $A$ and $B$ . Find the difference between their medians.
Show the worked solution
1. Step 1: Read each plot $A$ : $\text{min} = 6$ , $Q_1 = 12$ , $\text{median} = 20$ , $Q_3 = 26$ , $\text{max} = 38$ $B$ : $\text{min} = 16$ , $Q_1 = 26$ , $\text{median} = 32$ , $Q_3 = 40$ , $\text{max} = 50$
2. Step 2: Subtract the medians $\mathstrut 32 - 20$ $\text{Difference} = 12$
Question 5How many: a quarter of the data in each part
The box-and-whisker plot shows the times, in minutes, that $60$ students took to finish a task. Estimate the number of students who took more than $24$ minutes.
Show the worked solution
1. Step 1: The five values split the data into four quarters: above Q3 = 24 is a quarter of the dataA quarter of the students.
2. Step 2: A quarter of 60 $\dfrac{1}{4} \times 60 = 15$
Question 6How many: a quarter of the data in each part
The box-and-whisker plot shows the times, in minutes, that some students took to finish a task. $50$ of the students took less than $26$ minutes. Find the number of students who did the task.
Show the worked solution
1. Step 1: The lower whisker (minimum to Q1 = 26) holds a quarter of the dataA quarter of the students took less than $26$ minutes.
2. Step 2: So the total is 4 times that numberTotal $= 4 \times 50$ $= 200$

More on statistics

Notes: Statistics Worksheet with answers (PDF)

Endless questions on box-and-whisker plots

A free account gives you new questions every time, step-by-step help, and tracks what you've mastered.

Start free

Worked example

The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the median.

Step 1 of 2

Read the five values: the whisker ends, the box ends and the line in the box

\text{min} = 12

Q_1 = 20

\text{median} = 26

Q_3 = 34

\text{max} = 46

Questions

Question 1Read a box plot

The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the range.

Show the worked solution

Step 1: Read the five values: the whisker ends, the box ends and the line in the box $\text{min} = 22$ , $Q_1 = 30$ , $\text{median} = 34$ , $Q_3 = 42$ , $\text{max} = 48$
Step 2: Range = the whiskers' full length $\mathstrut \text{Range} = 48 - 22$ $\text{Range} = 26$

Question 2Read a box plot

The box-and-whisker plot shows the times, in minutes, that students took to finish a task. Find the range.

Show the worked solution

Step 1: Read the five values: the whisker ends, the box ends and the line in the box $\text{min} = 14$ , $Q_1 = 22$ , $\text{median} = 28$ , $Q_3 = 36$ , $\text{max} = 42$
Step 2: Range = the whiskers' full length $\mathstrut \text{Range} = 42 - 14$ $\text{Range} = 28$

Question 3Compare two box plots

The box-and-whisker plots show the times, in minutes, taken by two groups, $A$ and $B$ . Find the difference between their medians.

Show the worked solution

Step 1: Read each plot $A$ : $\text{min} = 12$ , $Q_1 = 20$ , $\text{median} = 26$ , $Q_3 = 34$ , $\text{max} = 46$ $B$ : $\text{min} = 8$ , $Q_1 = 16$ , $\text{median} = 19$ , $Q_3 = 27$ , $\text{max} = 36$
Step 2: Subtract the medians $\mathstrut 26 - 19$ $\text{Difference} = 7$

Question 4Compare two box plots

The box-and-whisker plots show the times, in minutes, taken by two groups, $A$ and $B$ . Find the difference between their medians.

Show the worked solution

Step 1: Read each plot $A$ : $\text{min} = 6$ , $Q_1 = 12$ , $\text{median} = 20$ , $Q_3 = 26$ , $\text{max} = 38$ $B$ : $\text{min} = 16$ , $Q_1 = 26$ , $\text{median} = 32$ , $Q_3 = 40$ , $\text{max} = 50$
Step 2: Subtract the medians $\mathstrut 32 - 20$ $\text{Difference} = 12$

Question 5How many: a quarter of the data in each part

The box-and-whisker plot shows the times, in minutes, that $60$ students took to finish a task. Estimate the number of students who took more than $24$ minutes.

Show the worked solution

Step 1: The five values split the data into four quarters: above Q3 = 24 is a quarter of the dataA quarter of the students.
Step 2: A quarter of 60 $\dfrac{1}{4} \times 60 = 15$

Question 6How many: a quarter of the data in each part

The box-and-whisker plot shows the times, in minutes, that some students took to finish a task. $50$ of the students took less than $26$ minutes. Find the number of students who did the task.

Show the worked solution

Step 1: The lower whisker (minimum to Q1 = 26) holds a quarter of the dataA quarter of the students took less than $26$ minutes.
Step 2: So the total is 4 times that numberTotal $= 4 \times 50$ $= 200$