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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
6 - 83
9 - 1110
12 - 147
15 - 177
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
9 - 123
13 - 164
17 - 209
21 - 243
25 - 283
29 - 326
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
14 - 185
19 - 238
24 - 284
29 - 334
34 - 3811
39 - 4310
44 - 489
49 - 539
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?

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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.]"

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?"

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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.

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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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