Mean, Median & Mode

What Your Child Is Learning

When most of us say "average," we mean one thing. In maths, there are actually three different types of average, and your child needs to know all of them. Each one answers the question "What's a typical value?" in a slightly different way.

Mean

The one you probably remember. Add up all the values, then divide by how many there are. The mean uses every single piece of data, which makes it thorough — but it also means one extreme value can pull it way up or way down.

Median

Put the values in order. The median's position is \((n + 1) \div 2\), where \(n\) is how many values there are. For 7 values that's the 4th. For 2, 5, 8, 12 it's \((4 + 1) \div 2 = 2.5\), so halfway between 5 and 8, which is 6.5. If the position ends in .5, the median is halfway between the two values either side. The median is brilliant when you have extreme values (outliers), because it ignores them. It just cares about what's in the middle.

Mode

The mode is the value that appears most often. If two values tie for most often, there are two modes. If no value repeats, there is no mode. The mode is the only average that works for non-numerical data (like "What's the most popular school lunch?").

Schools teach all three together so students can compare them and understand that different situations call for different averages. This is actually a really important real-world skill — the mean salary in a company with one very highly paid CEO tells a very different story from the median salary.

How Schools Teach It Now

The teaching approach emphasises understanding when to use each average, not just how to calculate them.

Step 1: Calculate All Three

Given a dataset, students practise finding the mean, median, and mode of the same data. This builds fluency with each method.

Step 2: Compare and Discuss

Students look at cases where the three averages give different answers and discuss which one best represents the data. For instance, house prices in a street where one mansion inflates the mean — the median is more useful there.

Step 3: Range

Alongside the three averages, students learn the range: the difference between the highest and lowest values. The range measures how spread out the data is — it's not an average, but it's always taught alongside them.

Step 4: Choosing the Right Average

Exam questions often ask which average suits the data best, and why. This is where students need to think, not just calculate. Schools spend real time on this reasoning.

Common Mistakes to Watch For

• Forgetting to sort before finding the median. The median is the middle value when the data is in order. If your child picks the middle number from an unsorted list, they'll almost certainly get the wrong answer. Always sort first.
• Confusing mean and median. "Add them up and divide" is the mean. "Find the middle one" is the median. A helpful memory trick: mean = everything added up; median = middle (like the central reservation in a road — it's in the middle).
• Thinking there's always exactly one mode. There can be no mode (if nothing repeats), one mode, or multiple modes (if several values tie for most frequent). Students sometimes panic when there isn't a clean single answer.
• Dividing by the wrong number for the mean. If the data is 3, 7, 7, 9, 14, there are 5 values. Students sometimes divide by the largest value, or by the number of different values. It's always the total count of all the numbers, including repeats.

Try It Together

Let Them Practise

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