# Averages and Range - Level 4

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

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This is level 4; Mixed 'wordy' questions. You can earn a trophy if you get at least 7 questions correct.

 1. Ricky is 6 years old. Mel and Kim are both three years older than Ricky. Jaz is 24 . What is the mean of their ages? 2. The highest mark in the Science test was 89. Three students scored 67 which was four marks higher than the lowest score. What was the range of scores? 3. Five boys took part in a sponsored swim. Here is the number of lengths they completed: 8 13 6 6 10. What was the median number of lengths completed? 4. What is the difference between the mean and the median of the following set of numbers {5, 26, 6, 5, 8} 5. The weights of six dogs in kilograms are: 12.1, 14.3, 10.8, 14.0, 10.7 and 15.5. Calculate the mean weight correct to one decimal place. 6. Calculate the range of weights in kilograms of the dogs given in question 5. 7. Calculate the median of the weights of the dogs given in question 5 correct to two decimal places. 8. Take away four discs that have a mean of 6. Which disc is left? 9. Take away six discs whose mean and median are the same whole number. Which disc is left? 10. Mac has taken seven maths exams this year. His average mark is 78%. What mark must he get on the eighth exam to raise his average to 80%?
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This is Averages and Range - Level 4. You can also try:
Level 1 Level 2 Level 3 Level 5 Level 6 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.

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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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#### Equatero

Find the mathematical expression from a series of guesses and clues. This is the numerical version of the extremely popular internet sensation Wordle and UK TV quiz show called Lingo.

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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.

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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.

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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.