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Mean Average: Free Printable Worksheet for Year 6
- ForYear 6
- StageKey Stage 2
- CostFree
- FormatPrintable PDF
Mean Average is a free printable maths worksheet for Year 6 (ages 10 to 11). Children find the mean of sets of numbers by adding them up and dividing by how many there are. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown-up notes, help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children find the mean of a series of number sets. Some sets have three numbers, and others have four, five or six. Some go up in steps of two, and one set uses tens. Two sets have a number that appears more than once, so children must decide how to count it. There is space to answer each question.
- 4, 6, 8
- 3, 5, 7, 9
- 10, 12, 14, 16, 18
- 2, 2, 5, 7, 9
- 11, 13, 15, 17
- 20, 30, 40
- 6, 8, 9, 9, 13
- 1, 3, 5, 7, 9, 11
A worked example
Find the mean of 22, 25, 31 and 26.
This question is not on the sheet. It shows two ways to reach the same mean.
Method 1: add, then divide- Add the numbers: 22 + 25 + 31 + 26 = 104.
- Count how many numbers there are. There are 4.
- Divide the total by 4: 104 ÷ 4 = 26.
- Guess a mean of 25.
- Find how far each number is from 25: 22 is 3 below, 25 is 0 away, 31 is 6 above, 26 is 1 above.
- Add the gaps: minus 3, plus 0, plus 6, plus 1 makes plus 4. Share 4 across 4 numbers to get 1 each, so the mean is 25 + 1 = 26.
How to think about the mean
Think fair share
Imagine every number is a pile of counters. The mean is how many each pile would hold if you shared all the counters out evenly.
Total first
Add every number in the set. Write the total down before you do anything else. This is the amount to be shared.
Count the numbers
Count how many numbers are in the set. Count a repeated number each time it appears. This is how many groups you share into.
Divide and check
Divide the total by the count. Then check that your answer sits between the smallest and largest number in the set.
What is a mean?
The mean is one kind of average. It tells you what each number would be if they were all made equal. You find it by adding the numbers and dividing by how many there are. Because every number is used, one very big or very small number can pull the mean up or down.
Other averages include the median, which is the middle value when numbers are in order, and the mode, which is the most common value. Year 6 children work on the mean in the Statistics strand of the National Curriculum for England. Understanding what it means matters as much as getting the sum right.
Skills and curriculum link
- Finding the mean
- Adding a set of numbers
- Dividing by the count
- Estimating and checking
- Explaining reasoning
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Statistics | Year 6 |
What children will be able to do
- I can add up a set of numbers.
- I can divide by how many numbers there are.
- I can find the mean.
Ideas that help with the mean
- Total firstThe mean always starts with the total of all the numbers. Adding carefully, perhaps in pairs, makes the later steps easier.
- Count the numbersThe number you divide by is how many numbers are in the set, not the total or the biggest number.
- Fair share picturePicture the numbers as piles of counters being levelled out. Some piles give counters away and some receive them until all are equal.
- Sense checkThe mean cannot be smaller than every number in the set or larger than every number in the set. If it is, something went wrong.
Key words
- MeanThe fair share of a set of numbers. Add them up, then divide by how many there are.
- AverageA single number that tries to show what a set of numbers is like overall.
- TotalThe answer when you add all the numbers together.
- DivideShare an amount into equal groups.
- SetA group of numbers that belong together.
- DataInformation, often numbers, that we collect and look at.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
- Read the first set of numbers together. Ask your child to guess roughly where the mean might be, before any sums.
- Remind them to add first, then divide. They should count how many numbers are in the set before dividing.
- Check the answer sits between the smallest and largest number. Then compare with page 2 and ask, "How did you work that out?"
- Come back another day and redo any questions that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Use counters to make each number as a pile. Put all the counters together, then share them out evenly into as many equal groups as there are numbers. Start with the sets that have three numbers. Say each step aloud as you go.
To stretch confident children
Make up a set of five numbers with a mean of 10. Think about what total the five numbers must make. Then find a different set with the same mean. Swap with a friend and check each other's sets.
Make it a game
Roll a die five times and write down each roll. Add the rolls, then divide the total by 5 to find the mean. The mean may not be a whole number. Play with a friend and compare whose mean is higher.
Mistakes to watch for
Watch forA child divides by the total, or by the biggest number, instead of by how many numbers there are.
Try thisAsk them to count the numbers in the set and write the count in a circle before they divide.
Watch forWith a set such as 22, 22, 25, a child counts the repeated number only once.
Try thisSay that each number is its own pile. Draw a pile for every number, including the repeats, then count the piles.
Watch forA child gets a mean that is larger than every number in the set.
Try thisUse the sense check. Ask, "Can a fair share be bigger than every number?" Then add the numbers again and look for a slip.
Talk about it
- How do you find the mean of a set of numbers?
- What does the mean tell you about the numbers?
- What do you think happens to the mean if one number gets bigger?
- Why must the mean sit between the smallest and the largest number?
- How could counters help you explain the mean to someone younger?
- Where might you see an average in real life?
Take it off the page
Counter sharing
Use dried pasta or buttons. Make uneven piles, then share them out until every pile is equal. Count how many are in each pile. That number is the mean.
Family shoe sizes
Write down each person's shoe size at home. Add them up and divide by the number of people. Talk about whether the answer matches anyone's real size.
Dice challenge
Roll a die ten times and record the scores. Find the mean. Then roll again and see whether the mean is close to the first one.
Who it is for
Parents
Sit beside your child for the first set, then let them lead. About 15 minutes is plenty. If they get stuck, give them counters to share out evenly. Ask them to explain each step rather than only giving the answer.
Teachers
Use it as a starter, a plenary after teaching the mean, an early finisher task or homework. Page 2 has support, stretch and answers for mixed groups. It needs no preparation beyond printing. The sets with repeated numbers are good talking points.
Home educators
Print it as part of a wider maths plan on statistics and averages. It pairs well with real data from daily life, such as family heights or dice rolls. You can print it again for revision or for brothers and sisters.
Where this fits
Before the mean, children need to add several numbers accurately and divide by a single digit number. They also meet simple data in tables and charts in earlier years. Sharing objects into equal groups is the idea underneath the mean.
After this, children can look at other averages such as the median and the mode. They can also compare sets of data and decide which average describes them best. In Key Stage 3 they build on this with larger data sets and more careful interpretation.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How do you find the mean?
- What does the mean tell you about the numbers?
- What happens to the mean if one number gets bigger?
Questions parents and teachers ask
- What age is Mean Average for?
It is written for Year 6 (ages 10 to 11), in Key Stage 2. Children who are confident with adding several numbers and dividing can use it. Younger confident children may enjoy it too, with some help.
- What will children practise?
Children practise finding the mean. They add the numbers in a set, count how many there are and divide the total by that count. They also check that the mean sits between the smallest and largest number.
- How long does it take?
It takes about 15 minutes for most children. Work through the first set together, then let them try alone. Short sessions work better than long ones, so stop and come back another day if needed.
- What if it feels too hard?
Use counters to share the total out evenly into equal groups. Start with the sets that have fewer numbers. Say each step aloud. Page 2 has more ideas for children who find it hard.
- Does it include answers?
Yes. Page 2 is for the grown-up and includes the answers, as well as notes on how to use the sheet, help for children who find it hard and a stretch idea.
- Is it suitable for classroom use?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 supports mixed ability groups.
- Is it free and screen free?
Yes. It is free to print for home and classroom use. It needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays. Black and white printing is fine.
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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.