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Averages - Level 5

Test your understanding of averages with this self marking quiz about mean, median and range.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Description Help More Averages

This is level 5; Mean, median, mode and range from a frequency table. You can earn a trophy if you get at least 9 questions correct. 

Give the answers to questions marked with an asterisk (*) to three significant figures.

Shoe SizeFrequencyWorking

This table shows the number of pairs of shoes of various sizes in the stock room of a shoe shop.

Find the the modal shoe size: CorrectWrong

Find the range of shoe sizes. CorrectWrong

What is the mean shoe size*? CorrectWrong

What is the median shoe size? CorrectWrong

Number of EggsFrequencyWorking

The Harrow Hens were in a good egg-laying mood. The table shows the number of eggs laid in each of the Harrow hen houses.

Find the modal number of eggs in a hen house. CorrectWrong

Find the range of the number of eggs in a hen house. CorrectWrong

What is the mean of the number of eggs in a hen house*? CorrectWrong

What is the median of the number of eggs in a hen house? CorrectWrong

Number of PassengersFrequencyWorking

Inspector Blakey recorded the number of passengers on each bus that passed a particular bus stop. The data is shown in the table.

What is the mean number of passengers per bus*? CorrectWrong

If one of the buses that passed the bus stop was selected at random, what is the most likely number of passengers to be on that bus? CorrectWrong

How many buses had more than the median number of passengers? CorrectWrong

The next bus to pass the bus stop was almost full. The number of passengers was recorded and Blakey noticed that the range of the data was now 10. How many passengers were on this last bus? CorrectWrong


This is Averages - Level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6


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.

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.

Please contact me if you have any suggestions or questions.

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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 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 the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School:

"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

Featured Activity

Roman Numerals Jigsaw

Roman Numerals Jigsaw

This is a wonderful activity for someone who does not know Roman numerals. By completing the activity an understanding of the symbols develops and a great sense of achievement is enjoyed.


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.

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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.


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:


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.]"

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.


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Description of Levels



Level 1 - Mean from a list

Level 2 - Range and mode from a list

Level 3 - Median from a list

Level 4 - Mixed 'wordy' questions

Level 5 - Mean, median, mode and range from a frequency table

Level 6 - Mean, median, mode and range from a bar chart

More Averages A wide range of interactive activities, puzzles, lesson starters and videos about mode, median, mean and range.

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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To find the mean of a set of values add them together then divide by the number of values.

Example: find the mean of 8,9,10: 8+9+10=27, 27÷3=9: The mean is 9


To find the median of a set of values arrange them in order then choose the middle value. If their are two middle values select the answer that is half way between those values.

Example: find the median of 4,12,7,6: In order 4,6,7,12: 6+7÷2: The median is 6.5

A formula for finding which is the middle value if there are N values is (N+1)/2. You can see why there is an 'add one' here.


The mode of a set of values is the value that occurs most times.

Example: find the mode of 2,4,4,1: The mode is 4.


The range of a set of values is the smallest value subtracted from the largest.

Example: find the range of 2,4,4,1: 4-1=3: The range is 3.

More Averages activities.

Mean, median and mode song.

The video above is from MathsWatch

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.

Log in Sign up