Four words, four quick rules, and one twist that accounts for most of the lost marks. Mean, median, mode and range are among the most reliable marks in the paper once a child can separate them.
Maths carries 25% of the marks, according to the partnership entrance test page. Almost all of it arrives as worded problems rather than bare calculations, which is the part that catches children out.
The four, in one table
| Word | What to do | Memory hook |
|---|---|---|
| Mean | Add them all up, divide by how many | The "average" people usually mean |
| Median | Put in order, take the middle one | Median is the middle of the road |
| Mode | The one that appears most often | Mode and most both start with mo |
| Range | Largest minus smallest | How far it stretches |
The single most common error is not arithmetic. It is answering the wrong one of the four because the child read the question too quickly. Underline the word before calculating.
All four on one set of numbers
Take: 2, 4, 5, 7, 7, 11
- Mean: they add to 36, and there are 6 of them. 36 divided by 6 is 6.
- Median: already in order. With six numbers there are two in the middle, 5 and 7, so take their mean: 5 plus 7 is 12, divided by 2 is 6.
- Mode: 7 appears twice and everything else once, so the mode is 7.
- Range: 11 minus 2 is 9.
Note that the mean and the median are both 6 here, which is a useful reminder that getting the same number twice does not mean you have made a mistake.
The median rule children forget
Two things go wrong with the median, and both are habits rather than understanding.
- Not putting the numbers in order first. The middle of the list as printed is not the median. Reorder, every time, without exception.
- An even number of values. With no single middle, take the two middle numbers and find the mean of those.
The twist: working backwards from the mean
This is the question that separates the field, and it comes up often.
The mean of five numbers is 8. Four of them are 5, 7, 9 and 10. What is the fifth?
Children try to do something clever with 8. The move is simpler than that: turn the mean back into a total.
- If the mean of five numbers is 8, the total must be 5 times 8, which is 40.
- The four known numbers add to 5 plus 7 plus 9 plus 10, which is 31.
- The missing number is 40 minus 31, which is 9.
Mean times how many gives the total. That one sentence unlocks every backwards mean question, including the ones about a new score changing a class average.
Habits that bank the marks
- Underline which of the four is being asked for before touching the numbers.
- Reorder before finding a median. Always.
- Count how many numbers there are and write it down. You need it for the mean and for the median.
- Sanity check the mean. It must sit between the smallest and largest value. If it does not, something has gone wrong.
See our guide to 11+ maths topics.
See where your child stands today
Timed sections in the GL Assessment format, marked instantly, with a topic-by-topic breakdown. No sign-up to start.
Most of these marks are lost to reading, not maths
Averages are among the most reliable marks in the maths section, and children still lose them. Almost never because the arithmetic defeated them. They answer the wrong one of the four, because they read the question at speed and saw the word average.
That connects to the thing I see across the whole paper. The majority of the 11+ maths is worded problems, so a child has to comprehend what is being asked before any formula comes into it. The speed of answering is what causes a lot of children to make mistakes, because they cannot parse the question and then decide what to apply quickly enough.
So the habit I would build here is small and it pays well. Underline the word, mean or median or mode or range, before touching a single number. It costs a second and it protects a mark the child has already earned.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
What is the difference between mean, median, mode and range?
The mean is the total divided by how many numbers there are. The median is the middle value once the numbers are in order. The mode is the value that appears most often. The range is the largest minus the smallest.
How do you find the median of an even set of numbers?
Put the numbers in order, then take the two middle values and find their mean. For 2, 4, 5, 7, 7 and 11 the middle two are 5 and 7, so the median is 12 divided by 2, which is 6.
How do you find a missing number when you know the mean?
Turn the mean back into a total. If the mean of five numbers is 8 then the total is 5 times 8, which is 40. If four of them add to 31, the missing number is 40 minus 31, which is 9. Mean times how many gives the total.
Why does my child get averages questions wrong?
Most often because they answered the wrong one of the four, having read the question too quickly, or because they looked for the median without putting the numbers in order first. Both are habits rather than gaps in understanding, so underlining the key word fixes a lot of them.
How can my child check an average is right?
The mean must always sit between the smallest and largest values in the set. If it does not, something has gone wrong in the addition or the division, and the check takes a couple of seconds.