Five children scored: 4, 7, 5, 9, 5
Total = 4 + 7 + 5 + 9 + 5 = 30
Mean = 30 ÷ 5 = 6
Mean, Median, Mode & Range for Year 6
Statistics questions appear on the reasoning papers almost every year. The concepts themselves are not hard — but children lose marks by mixing up mean and median, or by making arithmetic slips when adding up long lists of numbers. Here's how each one works.
The Mean (Average)
The mean is what most people call “the average”. Add up all the values, then divide by how many there are.
A useful sense-check: the mean should always be somewhere between the smallest and largest values. If it’s not, something has gone wrong.
The Median (Middle Value)
The median is the middle value when all numbers are put in order. If there’s an even number of values, it’s the mean of the two middle ones.
Scores: 4, 7, 5, 9, 5
In order: 4, 5, 5, 7, 9
Median = 5 (the middle value)
The most common mistake? Forgetting to put the numbers in order first. Without ordering, children just pick the number that happens to be in the middle of the list as written.
The Mode (Most Common)
The mode is the value that appears most often. A data set can have more than one mode, or no mode at all if every value is different.
Scores: 4, 7, 5, 9, 5
Mode = 5 (it appears twice; everything else appears once)
Top tip: “mode” sounds like “most”. The mode is the most frequent value.
The Range
The range is the difference between the largest and smallest values. It tells you how spread out the data is.
Scores: 4, 7, 5, 9, 5
Range = 9 − 4 = 5
SATs-Style Example Question
“The mean of four numbers is 8. Three of the numbers are 6, 9 and 11. What is the fourth number?”
If the mean is 8 and there are 4 numbers:
Total must be 8 × 4 = 32
Sum of three known numbers: 6 + 9 + 11 = 26
Fourth number = 32 − 26 = 6
This is a classic “working backwards” question. The SATs love it because it tests whether children truly understand what the mean represents, not just whether they can follow the formula.
Common Mistakes to Watch For
- Confusing mean and median — mean is calculated (add then divide); median is found by ordering and picking the middle.
- Not ordering for the median — must be in ascending order first.
- Arithmetic errors on the total — when adding a long list of numbers, encourage your child to add in pairs or use column addition.
- Dividing by the total instead of the count — the mean is total ÷ how many values, not total ÷ total.
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