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Averages and Range - Level 6

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

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This is level 6; Mean, median, mode and range from a grouped 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.

1.
Days with rainFrequencyWorkingWorking
4 - 67
7 - 914
10 - 128
13 - 157
Umbrella

This table shows the number days rain was recorded during the main summer holiday weeks in recent years.

Find the the modal group: CorrectWrong

Find the range of the data. CorrectWrong

Estimate the mean amount* CorrectWrong

In what group is the median? CorrectWrong

2.
Goals ScoredFrequencyWorkingWorking
14 - 177
18 - 217
22 - 257
26 - 298
30 - 339
34 - 374
Football

The table shows the number of goals scored in Term 1 by a number of school football teams.

Find the modal group. CorrectWrong

Find the range of goals scored. CorrectWrong

What is the mean number of goals scored*? CorrectWrong

In which group is the median? CorrectWrong

3.
Tins of PrunesFrequencyWorkingWorking
9 - 133
14 - 184
19 - 235
24 - 2812
29 - 337
34 - 3811
39 - 436
44 - 483
Prune

The table shows the number of tins of prunes sold each week since a promotion began. Estimate the mean number of tins sold per week*. CorrectWrong

If one of the weeks was selected at random for further analysis, what is the most likely 'tins of prunes' group for that week to be in? CorrectWrong

Find the range of the data. CorrectWrong

In which group is the median? CorrectWrong

Check

This is Averages and Range - Level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7

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.

Why am I learning this?

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 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

Comment recorded on the 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy:

"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

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Arrange the nine pieces of the puzzle on the grid to make the given polygon. Level one is for those learning the names of shapes while other levels are for those who like a challenge!

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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.

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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 is a mirror site at Transum.info that contains 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.]"

Gabriel Simamora, Harlaw Academy (Scotland)

Friday, February 19, 2021

"How do you answer question 10 to level one?
Thanks.

[Transum: Clue, let the age of the youngest person in the queue be x.]"

Transum,

Saturday, October 2, 2021

"If the average of a, b, c and d are a, what is the average of b, c and d?"

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

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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 grouped frequency table

Level 7 - 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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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Reminders

Mean

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

Median

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.

Mode

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.

Range

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.

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.

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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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