Getting the numbers out is half the question: averages
The Short Answer
Mean, median, mode and range are four short jobs. What the 11+ adds is that the numbers arrive buried — inside a frequency table, on a chart with a key, or not at all, with the mean given and a missing value to find. Getting the data out is half the question, and the check that catches most errors is asking whether the answer sits inside the set.
What do these questions ask?
For a mean, a median, a mode or a range. Four short jobs your child has known since Year 4:
- Mean — add them all up, divide by how many
- Median — the middle one, in order
- Mode — the one that appears most often
- Range — biggest take away smallest, and it is a measure of spread, not an average
None of that is where the marks go.
The paper stops handing you the numbers
By Year 5 the values arrive buried. They are inside a frequency table. They are on a chart with a key and an awkward scale. Sometimes they are not given at all — the paper supplies the mean and asks your child to work backwards.
Getting the data out is half the question, and it is where nearly every error lives.
The routine
Which average is it? Underline the word.
Get the numbers out and put them in order.
Do that average's one job.
Check it sits inside the set.
Rung four does more work than it looks. When your child has pulled eight numbers off a line graph, the likeliest mistake is not the division — it is miscounting how many there were. A mean that lands outside the data says so instantly.
Frequency tables
Working backwards from a mean
The move that unlocks these: mean × how many = the total.
Four numbers are 6, 9, 11 and 14. A fifth makes the mean 10.
Five numbers with a mean of 10 must total 50. The four given add to 40. So the fifth is 10.
Two steps, neither hard — and the whole difficulty is recognising the first one.
Where do pupils lose marks?
Counting rows instead of values on a frequency table.
Miscounting how many numbers there were, which the inside-the-set check catches.
Forgetting to order before finding a median.
Treating the range as an average.
Try it yourself
Get the numbers out and put them in order first. Then do that average's one job.
- Find the mean, median, mode and range of 3, 7, 7, 9, 14.
- Five numbers have a mean of 8. What do they add up to?
- Four numbers are 6, 9, 11 and 14. A fifth makes the mean 10. What is it?
- A frequency table shows 3 pupils scored 2, 4 pupils scored 5, and 5 pupils scored 3. How many pupils, and what is the total score?
- Why is checking the answer sits inside the data worth doing?
- Mean 8, median 7, mode 7, range 11. In order they are already 3, 7, 7, 9, 14 — the median is the middle one, the mode is the repeated one, and the range is 14 − 3.
- 40. The mean times the number of values gives the total, which is the key to every backwards question.
- 10. Five numbers with a mean of 10 total 50. The four given add to 40, so the fifth is 10.
- 12 pupils, total 41. Multiply each score by its frequency — 2×3, 5×4, 3×5 — then add. Note that 12 is the number of pupils, not the number of rows, which is the commonest slip on frequency tables.
- Because the likeliest error is not the division but miscounting how many values there were. A mean that falls outside the data announces that immediately, and it takes a second to check.
How much practice does this type need at home?
Use real numbers your child cares about — goals scored, minutes of reading, scores in a game over a week. Ask for the mean and then the median, and ask which one describes the week better.
That last question is worth more than it looks. A child who can say why one average suits a set better than another understands what an average is for, and will not confuse the four under pressure.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why is getting the data out the hard part?
Because the paper stops giving you a neat row of numbers. The values sit in a frequency table, or have to be read off a chart with an awkward scale, and by the time your child has extracted them the arithmetic is trivial. Most of the time on these questions should go on the extraction, which is also where nearly all the errors are.
How do frequency tables catch children out?
By making them count rows instead of values. A table showing three pupils scored 2 has three values of 2 in it, not one. So the number of values is the sum of the frequencies, and the total is each score multiplied by its frequency. Children who add the score column and divide by the number of rows get a plausible answer that is wrong.
What does a backwards question look like?
The mean is given and one value is missing. Multiply the mean by how many values there are to get the total, subtract the values you have, and what remains is the missing one. It is two steps and neither is hard — the difficulty is recognising that mean times count gives the total, which is worth saying aloud until it is automatic.
Is the range an average?
No, and it is worth being clear because questions ask for it alongside the three averages. The range measures how spread out the data is — biggest take away smallest. An average is a single value standing in for the set; the range describes how far the set stretches. They answer different questions.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
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