# Averages and Range - Level 7

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

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This is level 7; Mean, median, mode and range from a bar chart. 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 This bar chart shows the number of times each day a group of students drank water.Find the the mode of this data. Find the range of the data. What is the mean*? What is the median? 2 The number of dragon fruit collected from trees on an island are shown in the red bar chart.Find the modal number of fruit per tree. Find the range of the number of fruit per tree. What is the mean number of fruit per tree*? What is the median number of fruit per tree? 3 Percy Cod recorded the number of fish in each bucket early one morning on the dock of a small harbour. The data is shown in the bar chart.What is the average (mean) number of fish per bucket*? If one of the buckets was selected at random, what is the most likely number of fish to be in that bucket? How many buckets had less than the median number of fish? All of the fish from all of the buckets were cleaned and then put back in the buckets so that there were the same number of fish in each bucket. The few that may have been left over were considered to be waste and used to feed the penguins. How many fish were now in each bucket asuming the waste was a minimum?
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This is Averages and Range - Level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

## 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.

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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?

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Could we have some on angles too please?"

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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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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.]"

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?"

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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

Mixed Medians - Find the medians of sets of different types of numbers.

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.

## 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.