Calculating Averages

Understanding the concept

An average summarises a set of values. The mean is the sum divided by the number of values; median and mode are useful when values vary widely.

Start by identifying the quantities and units. Use a small example to understand the idea before attempting larger calculations.

Step-by-step method

Mean = sum of values ÷ number of values. To find the median, sort the values and choose the middle; for an even count, average the two middle values.

1. Read the question and underline what you must find.
2. Write down the given values and check their units.
3. Apply the relevant method one step at a time.
4. Estimate or reverse-check your answer before presenting it.

Quick-reference table

Use this reference to recognise common situations.

Four worked examples

Compare the different types of questions and the steps used to answer them.

Example 1: Weekly temperatures

Question or method: Find mean of 20, 22, 24 °C.

Example 2: Test scores

Question or method: Find mean of 60, 70, 80, 90.

Example 3: Median

Question or method: Find median of 3, 7, 9, 12.

Example 4: Outlier

Question or method: Compare 10, 11, 12, 13, 100.

Common mistakes

These errors are easy to make. Read each one and check your working.

• Dividing by the wrong number of observations.
• Finding the median without sorting first.
• Assuming the mean always represents a typical value.

Always ask whether your answer is reasonable for the original situation.

Practice questions

Try each question on paper before revealing the answer.

Review checklist

• Can you explain the key idea in your own words?
• Can you complete a worked example without looking at the solution?
• Can you identify a common mistake and correct it?
• Can you estimate whether your result is sensible?

Related lessons and tools

Continue with Everyday Maths lessons, or browse the CS17 Learning Centre. Where helpful, check calculations with the CS17 Calculator Workshop.