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Year 7 Maths

Statistics: Mean, Median, Mode

Learn three ways to describe the “middle” or “typical value” of a data set, and when to use each one.

Three Types of Average

An average is a single number that represents a whole data set. There are three common types:

Mean

Add all values, divide by how many

Most common average

Median

The middle value when ordered

Not affected by outliers

Mode

The most frequent value

Can have 0, 1, or more

Worked Examples

Data set: 3, 5, 7, 5, 10

1

Finding the Mean

Step 1: Add: 3 + 5 + 7 + 5 + 10 = 30

Step 2: Count: 5 values

Step 3: Divide: 30 ÷ 5 = 6

Mean = 6

2

Finding the Median

Step 1: Order: 3, 5, 5, 7, 10

Step 2: Middle value (5 numbers → 3rd value)

Median = 5

3

Finding the Mode

Step 1: Which value appears most often?

3 (once), 5 (twice), 7 (once), 10 (once)

Mode = 5

Even number of values? For the median, average the two middle values. E.g. for 2, 4, 6, 8: median = (4 + 6) ÷ 2 = 5.

When to Use Each Average

Use Mean when...

Data is spread evenly with no extreme outliers. Good for test scores, temperatures.

Use Median when...

There are outliers (very high or low values). Good for house prices, salaries.

Use Mode when...

You want the most popular or common choice. Good for shoe sizes, favourite colours.

Knowledge Check

Select the correct answer for each question. Questions get harder as you go!

Question 1

Find the mean of: 4, 8, 6, 2

Question 2

Find the mode of: 3, 7, 3, 9, 5, 3, 8

Question 3

Find the median of: 2, 9, 4, 7, 5

Question 4

Find the median of: 10, 3, 8, 5, 7, 1

Question 5

A data set has values: 2, 2, 3, 4, 4. How many modes does it have?

Question 6

Test scores: 65, 70, 72, 75, 80, 85, 150. Which average would best represent the “typical” score?

Question 7

The mean of 5 numbers is 12. What is their total?

Question 8

Data: 4, 7, 9, 11, 14, 7, 3, 7. Find the mean, median, and mode. Which value is the mode?

Question 9

Six students scored: 55, 60, 65, 70, 75, 80. A seventh student scored 100. What happens to the mean?

Question 10

Four students have a mean score of 70. A fifth student joins and the mean drops to 66. What did the fifth student score?

Key Concepts Summary