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# Box Plots

## An exercise on reading and drawing box-and-whisker diagrams which represent statistical data.

##### Level 1Level 2Level 3Exam-StyleDescriptionHelpMore Statistics

This is level 3: drawing box plots You can earn a trophy if you get at least 7 questions correct.

1. Drag the circles to create a box plot representing the number of minutes patients spent in a doctor's waiting room if the minimum waiting time is 6 minutes, the maximum is 31 minutes, the median time is 18 minutes, the lower quartile is 8 minutes and the upper quartile is 27 minutes.
2. The following is a list of times in minutes spent on social media by members of a chess team.
49, 30, 82, 39, 67, 44, 56.
Drag the circles to create a box plot representing this data on the grid above.
3. The following is a list of the lengths in metres of a tortoise's daily walks.
75, 84, 65, 94, 38, 74, 54, 57, 85, 67, 47.
Drag the circles to create a box plot representing this data on the grid above.
4. The following is a list of the number of times 15 people checked their email accounts in one day.
7, 28, 19, 48, 42, 9, 9, 21, 38, 19, 50, 17, 25, 8, 8.
Drag the circles to create a box plot representing this data on the grid above.
5. The following stem and leaf diagram shows the number of times 19 people said 'Happy New Year' on 1st January 2022.
1 0 1 3 5 1 3 4 7 0 0 2 3 3 6 8 9 2 3 3
Drag the circles to create a box plot representing this data on the grid above.
6. The following stem and leaf diagram shows the number of plastic bottles found in each of 23 bags of rubbish collected during a beach clean up operation.
2 5 6 0 3 6 7 9 1 6 9 2 6 9 1 3 5 9 1 5 8 2 3 3
Drag the circles to create a box plot representing this data on the grid above.
7. In Transum High School there are 27 classes. The following table show the number of students in those classes as a frequency table.
Class sizeFrequency
212
224
232
240
254
264
272
280
290
300
311
321
331
342
354
Drag the circles to create a box plot representing this data on the grid above.
8. The marks earned by 79 pupils in Year 11 of Transum High School in a mid-year exam are shown in the frequency table below.
MarkFrequency
523
531
541
552
561
572
582
594
606
614
628
6310
649
657
666
671
682
691
704
713
721
730
740
751
Drag the circles to create a box plot representing this data on the grid above.
9. The lengths (running time) of some instructional videos are shown in the cumulative frequency diagram. The shortest video lasted only three minutes.Drag the circles to create a box plot representing this data on the grid above. The times used in your box plot should be rounded to the nearest minute.
10. The following cumulative frequency graph shows the length of time in minutes, visitors watched an octopus swimming around a tank at an aquarium.Drag the circles to create a box plot representing this data on the grid above. Take the minimum time to be zero minutes and the other times used in your box plot should be rounded to the nearest minute.
Check

This is Box Plots level 3. You can also try:
Level 1 Level 2

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology:

"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales:

"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

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#### Remainder Race

A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Isabella,

Wednesday, April 26, 2017

"The formula for finding the median is a on N items is (N+1)/2. Why is there a 'plus one' in that formula?

[Transum: Good question Isabella. The answer is here.]"

Tuesday, April 21, 2020

"Is there a way to share the box plot level 1 activity without the answer key showing up at the bottom?

[Transum: Whoops, that's a glitch. I have corrected it now. Thanks for the information]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

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## Description of Levels

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Level 1 - Labeling a box plot diagram

Level 2 - Interpreting box plots

Level 3 - Drawing box plots

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Graphic Display Calculator - Here are instructions for drawing two box plots, one above the other on a GDC so that two data sets can be compared.

Reaction Times generate your own data by recognising odd and even numbers. Produce two box plots (one for even numbers and the other for odd numbers) on the same scale so that they can be compared.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Example

Fact worth knowing: If a value is more that 1.5 × IQR above the upper quartile or below the lower quartile it is considered to be an outlier.

If you are using a TI-Nspire CX calculator did you know that it can draw a box plot for you? See GDC Essentials.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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