Mean, Median, Mode and Range

Why we summarise data

Imagine you scored these marks on five spelling tests: 8, 6, 9, 7, 10. A friend asks, "How are you doing in spelling?" You could read out all five numbers, but it is faster and clearer to give a single number that sums up the whole set.

That single number is called an average or a measure of central tendency — a value that sits somewhere in the "centre" of the data and represents the group. In this lesson you will learn the three main averages — mean, median and mode — plus the range, which measures how spread out the data is.

These four ideas are the foundation of statistics. Once you can find them, charts and tables make far more sense. If you want practice reading data first, look at reading charts and graphs.

The mean

The mean is what most people call "the average". To find it:

Mean = (sum of all the values) ÷ (number of values)

Worked example 1

Find the mean of 8, 6, 9, 7, 10.

Step 1 — Add every value together. 8 + 6 + 9 + 7 + 10 = 40

Step 2 — Count how many values there are. There are 5 values.

Step 3 — Divide the total by the count. 40 ÷ 5 = 8

So the mean mark is 8. Notice the mean does not have to be one of the original numbers — it is a balancing point. If you stacked all the marks into one pile and shared them out equally between five tests, each test would get 8.

Worked example 2 (a decimal answer)

Find the mean of 3, 4, 4, 6.

Step 1: 3 + 4 + 4 + 6 = 17 Step 2: There are 4 values. Step 3: 17 ÷ 4 = 4.25

The mean is 4.25. Means very often come out as decimals, and that is perfectly normal — there is no rule that says the average of whole numbers must be whole.

The median

The median is the middle value once the numbers are placed in order from smallest to largest. Putting the data in order first is the step people forget most often, so always do it.

Worked example 3 (odd number of values)

Find the median of 9, 3, 7, 1, 5.

Step 1 — Put the numbers in order. 1, 3, 5, 7, 9

Step 2 — Find the middle. There are 5 values, so the middle one is the 3rd. That value is 5.

The median is 5. There are exactly two values below it (1, 3) and two above it (7, 9).

Worked example 4 (even number of values)

Find the median of 2, 8, 4, 10.

Step 1 — Put the numbers in order. 2, 4, 8, 10

Step 2 — There is no single middle. With 4 values, the two middle numbers are 4 and 8.

Step 3 — Take the mean of those two middle values. (4 + 8) ÷ 2 = 12 ÷ 2 = 6

The median is 6. A quick way to know which positions are in the middle: with n values, when n is even the middle two are positions n÷2 and n÷2 + 1.

The mode

The mode is the value that appears most often. "Mode" and "most" both start with mo, which is a handy memory trick.

Worked example 5

Find the mode of 5, 2, 5, 7, 5, 2, 9.

Count how many times each value appears:

Value	How many times
2	2
5	3
7	1
9	1

The value 5 appears most often (three times), so the mode is 5.

A data set can have no mode (if every value appears once), or more than one mode (if two values tie). The mode is the only average you can use with non-number data — for example, the most popular ice-cream flavour in a class.

The range

The range is not an average. It tells you how spread out the data is.

Range = largest value − smallest value

Worked example 6

Find the range of 14, 6, 22, 9, 6.

Step 1 — Find the largest value: 22 Step 2 — Find the smallest value: 6 Step 3 — Subtract: 22 − 6 = 16

The range is 16. A small range means the values are bunched closely together; a large range means they are widely scattered.

Putting it all together

Let's analyse one data set fully. The daily high temperatures (°C) for a week were: 18, 21, 18, 24, 30, 18, 19.

Measure	Working	Answer
Mean	(18+21+18+24+30+18+19) ÷ 7 = 148 ÷ 7	21.1 (1 d.p.)
Median	In order: 18, 18, 18, 19, 21, 24, 30	19
Mode	18 appears three times	18
Range	30 − 18	12

Why the choice of average matters

Each average can tell a different story, so picking the right one matters.

• The mean uses every value, which is great — but it gets pulled toward extreme values (called outliers). One unusually hot day of 30°C dragged the mean above most of the actual readings.
• The median ignores how extreme the outliers are; it only cares about position. That makes it the fairest choice when there are outliers, such as house prices or salaries where a few huge values would distort the mean.
• The mode is best when you want the most common or most popular result, and it is the only one that works for categories like colours or flavours.

So if a billionaire walks into a room of ten people, the mean wealth shoots up enormously, but the median barely moves — which is exactly why news reports often quote median income, not mean income.

Practice activity

Survey 8 to 12 classmates about something countable — for example, how many books they read last month, or how many minutes it takes them to get to school. Write your data set down, then:

1. Find the mean, median, mode and range.
2. Write one sentence saying which average best represents your group, and explain why.
3. Add one very large value (a deliberate outlier) and recalculate. Notice how much the mean changes compared with the median.

To extend your skills next, practise percentages made easy, which is the natural next step in handling real-world data.

Quick recap

The mean shares the total out equally, the median finds the middle of ordered data, the mode finds the most frequent value, and the range measures spread. Master these four and you can describe almost any set of numbers in a clear, honest way.