# Frequency Trees

## Use a frequency tree to show two or more events and the number of times they occurred.

##### Frequency TreesExam-StyleTree DiagramsDescriptionHelp VideoMore Probability

30 pupils from a class were asked if they owned a bicycle. There were 15 boys and 15 girls in the class. 8 boys and 2 girls owned bicycles. Show this information on this frequency tree.

Boys

Girls

Own bicycle

No bicycle

Own bicycle

No bicycle

28 people were asked which hot beverage they would prefer if they had to choose between tea and coffee. 9 men prefered tea and 1 men prefered coffee. 7 women prefered tea and 11 women prefered coffee. Show this information on this frequency tree.

Men

Women

Tea

Coffee

Tea

Coffee

In a hotel the rooms are either single or double. Of the 36 rooms that had a sea view, 34 of them were double. Of the 18 rooms that did not have a sea view, 13 of them were single. Show this information on the diagram.

Single

Double

Sea view

No sea view

Sea view

No sea view

The following two-way table shows the eating habits of the members of a large family

 Age: Eat breakfast Skip Breakfast 18 or less 8 1 Over 18 6 6

Complete the following frequency tree to show this information.

18 or less

Over 18

Eat breakfast

Skip Breakfast

Eat breakfast

Skip Breakfast

288 cats and 89 dogs took part (with the help of their owners!) in a food preference survey. Twice as many cats preferred fish to meat and a total of 196 animals preferred fish. Complete the following diagram with this information.

Cats

Dogs

Meat

Fish

Meat

Fish

Check

## 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 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

#### Tran Towers

A mathematical adventure game in the enigmatic home of Transum. Create your own map as you go deeper and deeper into this maze of rooms looking for the clues to find the treasure room.

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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:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/Maths/Activity/Probability/Frequency_Trees.asp?Level=1

## Description of Levels

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Level 1 - Completing a frequency tree from given information

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

Tree Diagrams - Calculate the probability of combined events using tree diagrams.

More on this topic including lesson Starters, visual aids and investigations.

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

The video above is from Mr Duncan www.999maths.com.

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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