Mean, Median, Mode and Range: Free Printable Worksheet for Year 7

Mean, Median, Mode and Range is a free printable worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Work out the four averages It comes from the Mini Minds Hub, a growing library of free printables from Jaques of London, the British games and toy company that has been making games for families since 1795.

It is two A4 pages. Page 1 is the activity for children. Page 2 is for the grown-up: it has notes on how to use the sheet, help for children who find it hard, a stretch idea, and the answers. Print it at home or in the classroom. Black and white printing works well.

What is on the sheet

This worksheet includes numbered questions with space to answer.

A look at what children will meet:

• Mean of 4, 6, 8, 10, 12
• Median of 3, 9, 5, 7, 1
• Mode of 2, 5, 5, 7, 9, 5, 3
• Range of 12, 4, 19, 7, 15
• Mean of 5, 7, 9, 3
• Median of 2, 4, 6, 8
• Mode of 6, 2, 6, 8, 2, 6
• Range of 18, 35, 22, 30

Who this is for

Year 7 (ages 11 to 12) in Key Stage 3.

Key Stage 3 covers Years 7 to 9, ages 11 to 14. Learners are moving from remembering facts to applying them, so tasks that ask for a reason or a method are worth more than quick answers. Use it at home, in class, on a rainy afternoon or at a family gathering.

What children practise

• Averages
• Ordering data
• Calculation

Find the mean, median, mode and range of small sets of numbers.

Learning focus and curriculum link

Subject: Maths: Statistics. Key stage: Key Stage 3. It supports the subject at this level through short, focused practice.

This sheet is a practice and play activity. It supports classroom learning and is not a replacement for it.

How to use it

1. Print both pages. Page 1 is for the child. Keep page 2 for the grown-up.
2. Practice after teaching the four averages. About 15 minutes, then mark together.
3. Work through the activity together the first time. Talk about each choice.
4. Check against the notes on page 2 and the answers.
5. Come back to it another day. Repeating a familiar activity builds confidence.

If it feels too hard

Write the numbers on cards and put them in order before finding the median or range.

To stretch confident children

Ask the child to write a set of five numbers with a mean of 10 and a mode of 8.

Make it a game

Roll a die ten times, record the numbers, and find all four averages.

Tips for parents and teachers

• Print on plain A4 paper. Black and white printing works too.
• Work through it together the first time, then let children try alone.
• Praise effort and thinking, not only correct answers.

A screen-free maths: statistics activity for Year 7

Children spend a lot of time on screens. This is a screen-free maths: statistics activity that needs only paper and a pencil. It works as quiet time after school, a rainy day activity, a holiday boredom buster or a calm moment before bed. Screen-free learning gives eyes a rest and gets children talking, thinking and writing by hand.

Free maths: statistics resources for teachers

Teachers can use this worksheet as a starter, a plenary, an early finisher task, a supply teacher resource, a homework task or a table activity. It needs no preparation beyond printing. The learning focus and skills are listed above so you can match it to your planning, and page 2 gives support and stretch ideas for mixed ability groups.

Maths: Statistics ideas for parents at home

You do not need to be a teacher to use this. Read the sheet through, sit with your child for the first go and let them lead. Short bursts of ten to fifteen minutes work better than long sessions. If you are looking for free maths: statistics worksheets for Year 7, or simple home learning for the weekend or school holidays, this is a good place to start.

Home education and tutoring

Home educators and tutors can print this as part of a wider maths: statistics plan. It pairs well with books, outdoor play and everyday talk. Because the sheet is free and printable, you can use it again for brothers and sisters or for revision a few weeks later.

Why it helps children learn

Hands-on, paper based activities slow learning down in a good way. Children read carefully, think before they answer and see their own progress on the page. Games and challenges add a reason to keep going. That mix of play and practice is why printable activities like this are popular with parents, teachers and home educators.

Why mean, median, mode and range matter

Every day, someone tells you an average. The average house price, the average temperature, the average score in the match. An average is a way of squashing a long list of numbers into one number that says something useful. Mean, median and mode are three different ways of doing that. Range tells you how spread out the numbers are.

The four ideas belong together because each one answers a different question. The mode asks what happens most often. The median asks what sits in the middle. The mean asks what the value would be if everything were shared out equally. The range asks how far the data stretches. A child who can find all four, and who can say which one best fits a situation, is doing real statistics and not only arithmetic.

The national curriculum for England treats this as core Year 7 work. Statistics sits inside the maths programme of study, and the Key Stage 3 wording names all four ideas. It also asks children to think about outliers, which are odd values that sit far from the rest and can drag an average somewhere unhelpful. This sheet gives children short sets of numbers to practise on, so that the methods become automatic and the thinking can start.

What the research says children find hard

There is less research on averages than on fractions, so we will be careful about what we claim. The best-known work we could open is by Susan Jo Russell and Janice Mokros, in Cambridge, Massachusetts. They gave a talk at the Third International Conference on Teaching Statistics in 1990, called "What's Typical? Children's and Teachers' Ideas About Average". It was a small interview study of 21 US children (seven in each of fourth, sixth and eighth grade) and eight teachers. That is a small group, and it is a US study, so it describes how some children think. It does not give a rate for all children in England. Still, what the interviews showed is useful to any adult helping with this sheet.

• Average as "what happens most". The researchers found four broad approaches to average. One was average as the mode. Five children and one adult in that group saw the average as the value that occurs most often. It worked well until they were asked to build a data set that did not use the average value. The authors say people in that group then met real difficulties.
• Average as "what is reasonable". Some children used values that made sense in real life, such as realistic prices, and they knew the average sits roughly in the centre of the data. But they treated it as an approximation, not an exact number.
• Average as the midpoint. Six children went for the middle of the data. The authors report that some people in this group even suggested that the median might be used as a shortcut for finding the mean. When children place values evenly either side of the mean, the mean, median and mode all come out the same. That is a trap, because real data is rarely so tidy.
• Average as a calculation. Five of the 21 children, all in sixth or eighth grade, and six of the eight teachers used "add them up and divide" to some extent. The authors say that people who knew only the procedure had great difficulty when asked to build a data set that fitted a given mean, because there is no way to use the procedure in reverse.

The authors draw a clear lesson. They write that teaching the algorithm as a separate procedure causes a short-circuit in the reasoning of many children, who give up sound intuitions about what is typical in order to follow a rule. They argue that children's own ideas should be built on, not replaced. One child in the study said she only knew how to get an average by adding up grades and dividing, and that she did not know how to do it with M&M sweets. That is the gap this sheet tries to close: knowing the steps is not the same as knowing what the number means.

None of this means your child is behind if they mix up the three averages. They are three words that sound alike, they all get called "average", and they are taught close together. Mixing them up is common. Short, repeated practice is our suggestion.

What Year 7 children are expected to learn

The national curriculum for England, in its Key Stage 3 mathematics programme of study, says pupils should be taught to describe, interpret and compare observed distributions of a single variable through:

• appropriate graphical representation involving discrete, continuous and grouped data
• appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

Children meet the mean earlier. The Year 6 programme of study says pupils should "calculate and interpret the mean as an average". So Year 7 builds on that and adds the median, the mode, the range and the idea of outliers. The word "interpret" matters. It is not enough to find a number. The curriculum also says pupils should "select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems". Choosing the right average for the job is exactly that kind of problem. This sheet practises the first half, finding each value correctly, and the stretch tasks begin on the second.

Why a game or activity can help

Short, repeated practice is what averages need, because each method is simple but easy to muddle. There are two kinds of evidence worth knowing, and it is fair to be clear about what each one shows.

First, research on memory. In experiments by Roediger and Karpicke, published in Psychological Science in 2006, the abstract reports that prior testing produced substantially greater retention than studying alone, when final tests came two days and a week later. On a test five minutes later, restudying did better. The students were not primary children, and the study was about remembering material, not about statistics. Ofsted's review of maths teaching says that long-term retrieval of core content should be a focus of teachers' and leaders' planning. Finding the median of a new set of numbers from memory, without looking at the method, is retrieval practice.

Second, a study of games. Researchers at Carnegie Mellon University found that preschoolers from low-income families who played a number board game for four sessions of 15 minutes improved their counting, number recognition, number comparison and number line estimation, and all of the gains remained nine weeks later. Children who played a similar game with coloured squares showed no improvement. That was a US study of young children and whole numbers. It does not show that a game improves Year 7 statistics. We mention it only as encouraging evidence that a short, structured game can be useful when it is built around the skill you want.

We have not found research on printable sheets for averages in particular. So we make a modest claim. The sheet gives focused repetition, and the dice game and stretch tasks give children a reason to care about the answers.

How to get the most out of Mean, Median, Mode and Range

1. Start with a story, not a rule. Take five numbers such as 3, 5, 5, 7 and 10. Ask your child: if these were five test scores, what score is typical? Let them argue first. Then show that the mode is 5, the median is 5, the mean is 6 and the range is 7.
2. Put the numbers in order first. Every median and every range starts with a sorted list. Write the numbers on small cards and move them into order. The sheet's support note suggests this for children who struggle.
3. Say what each answer means. Do not stop at "the mean is 6". Ask: what does that tell us? The mean is the amount each person would get if the total were shared out equally.
4. Work the first questions together, then let them try alone. Mark it together using page 2. Return to the sheet a few days later.
5. Try the dice game. Roll a die ten times, write the results down, and find all four values. Do it again and compare. Does the mean change much? Does the range?
6. Try the reverse task. Ask for five numbers that have a mean of 6 and a mode of 4. One answer is 4, 4, 6, 7 and 9. This is the construction idea from the research above, and it is harder than it looks.

Common mistakes, and what to say

• Not sorting before finding the median. For 9, 2, 7, 4, 5 the middle number as written is 7, but the median is 5. Say: put them in order first, then count in from both ends.
• Two middle numbers. With an even number of values there is no single middle. Find the two middle values, add them and halve. For 2, 4, 6, 10 the median is 5.
• Saying there is no mode. Some sets have no repeated value, and some have two modes. Both are fine. Say: it is allowed to have none or two.
• Range as the biggest number. Range is the biggest minus the smallest. For 3, 8 and 20 it is 17, not 20.
• Dividing by the wrong number. The mean divides the total by how many values there are, including any zeros. A zero still counts.
• Believing the mean is always the best average. Look at 2, 3, 3, 4 and 48. The mean is 12, but four of the five values are 4 or below. The median, 3, describes the group better. This is what the curriculum means by considering outliers.

Why teachers matter to us

We are a games company, and we have been making games since 1795. We do not think a printable replaces a teacher. When it comes to maths, the evidence says teachers matter a great deal. A 2011 report for the Sutton Trust found that during one year with a very effective maths teacher, pupils gain 40% more in their learning than they would with a poorly performing maths teacher. It also found that for poor pupils, the difference between a good teacher and a bad one is a whole year's learning.

That report also found that paper qualifications and personal characteristics tell us very little about how good a teacher will be. It says factors such as teaching experience, the university attended and advanced degrees explain less than 8% of teacher quality. A University of Bristol study of English pupils likewise found considerable variability in teacher effectiveness. Our reading is that great teaching is a craft seen in the classroom, and that the people who do it well deserve our thanks.

So the sheets are free for teachers. Use this one as a starter, a plenary or a cover lesson. If it saves you ten minutes, we have done our job.

A caution on the Sutton Trust figures: the report draws on US studies as well as English ones. The 40% compares a very effective teacher (at the 84th percentile) with a poorly performing one (at the 16th percentile). The figure that paper credentials explain less than 8% of teacher quality comes from US research. We use them as pointers, not as a promise about any one child.

Why education matters to us

Averages are everywhere in adult life, from wages and prices to health figures and election polls. A young person who can ask "which average is that, and is it a fair one?" is harder to mislead and better placed to make decisions. Games are one of the oldest ways of making practice feel like play, and Jaques of London has been making them for generations. The Mini Minds Hub aims to carry that on: free, screen-free, and simple enough for a parent at a kitchen table as well as a teacher at a desk.

Mean, Median, Mode and Range: 20 questions and answers

1. What is the difference between mean, median and mode?

The mean is the total divided by the number of values. The median is the middle value when the numbers are in order. The mode is the value that appears most often.

2. Which average should I use?

It depends on the question. The mode suits "what is most common". The median suits data with a few very high or very low values. The mean suits fair-share questions with no odd values.

3. How do I find the median of an even number of values?

Find the two middle values, add them and halve the result. For 2, 4, 6 and 10 the two middle values are 4 and 6, so the median is 5.

4. Can a set of numbers have two modes?

Yes. In 2, 2, 5, 5, 8 both 2 and 5 appear twice, so there are two modes. A set can also have no mode if nothing repeats.

5. What is the range?

The range is the largest value minus the smallest. It tells you how spread out the data is, not what is typical.

6. What is an outlier?

An outlier is a value far from the rest. The Key Stage 3 curriculum names the "consideration of outliers" as part of spread. In 2, 3, 3, 4 and 48, the 48 is an outlier.

7. Why does an outlier change the mean more than the median?

The mean uses every value in its total, so one huge value pulls it up. The median only cares about the middle position. In 2, 3, 3, 4 and 48 the mean is 12 but the median is 3.

8. Does a zero count when finding the mean?

Yes. A zero adds nothing to the total, but it still counts as one of the values you divide by.

9. Why do children mix up mean, median and mode?

All three get called "average", and the words sound alike. In the small Russell and Mokros interview study, children used different ideas of average, including "the most common value" and "the middle". Mixing them up is a normal stage.

10. What does the national curriculum say about averages in Year 6?

Pupils should "calculate and interpret the mean as an average". Year 7 adds the median, mode, range and outliers.

11. What does the national curriculum say about averages in Key Stage 3?

It lists "appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)".

12. How do I check a mean without a calculator?

Check that the answer is between the smallest and largest values. If it is not, something is wrong. Then multiply the mean by the number of values. You should get the original total.

13. Can the mean be a number that is not in the data?

Yes. The mean of 1, 2 and 6 is 3, which is not in the list. The median and the mode always come from the list, apart from the median of an even set, which can fall between two values.

14. Can the mean be bigger than every value?

No. The mean always sits between the smallest and largest value. If a child's answer is bigger than every number in the list, they have made a slip, and saying so aloud is a quick check.

15. How can I build a set of numbers with a given mean?

Multiply the mean by how many numbers you want to get the total. Then choose numbers that add up to that total. For five numbers with a mean of 6, the total must be 30.

16. Which stretch task is on the sheet?

Children build a set of five numbers with a given mean and mode. It practises working backwards, which is harder than working forwards.

17. What is the dice game?

Roll a die ten times, write down the results and find the mean, median, mode and range. Roll again and compare. It shows how data changes from one sample to the next.

18. Do games really help children learn?

Games give many quick repeats and make recall active. A study of preschoolers found that four 15-minute sessions with a number board game improved number skills, and the gains lasted nine weeks. That study was about whole numbers in preschool, so it is suggestive for averages and not proof. Ofsted's maths review also says retrieval of core content should be a focus of planning.

19. How often should we practise?

Little and often works better than one long session. The 2006 Roediger and Karpicke abstract reports that prior testing produced substantially greater retention than studying alone on tests two days and a week later. Come back to the sheet a few days after the first go.

20. Where can I find more Year 7 maths sheets?

See the More free printables section below, or browse all Year 7 maths printables in the Mini Minds Hub.

Sources

1. Department for Education, National curriculum in England: mathematics programmes of study (Year 6 statistics; Key Stage 3 statistics and aims): gov.uk.
2. Russell and Mokros, "What's Typical? Children's and Teachers' Ideas About Average", ICOTS 3 (1990): fpce.uc.pt.
3. Roediger and Karpicke, Psychological Science (2006): psychologicalscience.org.
4. Ofsted, Research review series: mathematics (2021): gov.uk.
5. Ramani and Siegler, Child Development (2008), reported by ScienceDaily: sciencedaily.com.
6. Sutton Trust, Improving the impact of teachers on pupil achievement in the UK, interim findings (2011): dera.ioe.ac.uk.
7. Slater, Davies and Burgess, University of Bristol CMPO Working Paper 09/212 (2009): bristol.ac.uk.

Frequently asked questions

What age is Mean, Median, Mode and Range for?

It is written for Year 7 (ages 11 to 12), in Key Stage 3.

What will children practise?

Find the mean, median, mode and range of small sets of numbers.

How do I use it?

Practice after teaching the four averages. About 15 minutes, then mark together.

What if it feels too hard?

Write the numbers on cards and put them in order before finding the median or range.

Is it free?

Yes. It is free to print for home and classroom use.

Is Mean, Median, Mode and Range suitable for teachers to use in class?

Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing.

Is this a screen-free activity?

Yes. It is a screen-free printable that needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays.

Can I use it for home education?

Yes. Home educators and tutors can use it on its own or as part of a wider plan. It is free to print again for brothers, sisters or revision.

How long does it take?

Most children finish page 1 in 10 to 20 minutes. The notes on page 2 suggest ways to make it shorter or longer.

Do I need to print in colour?

No. It prints well in black and white on plain A4 paper.

More free printables

More for Key Stage 3 | More maths: statistics printables | Free printable games | All Mini Minds Hub resources