The Weighted Mean
Revise The Weighted Mean for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. A weighted mean gives some values more importance than others by multiplying each by a weight.
Free downloads
These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
A weighted mean gives some values more importance than others, reflecting that they should count for more. This is a Higher-only topic.
Each value is multiplied by its weight, the products are added, and the total is divided by the sum of the weights. This gives \(\frac{\sum wx}{\sum w}\).
It is used where components contribute unequally, such as exam papers worth different percentages of a qualification, or a price index where some goods are bought more often than others. Dividing by the number of values rather than the sum of the weights is the standard error, and it produces an answer that is far too small.
Revision notes
The formula
Weighted mean \(= \frac{\sum wx}{\sum w}\), where \(w\) is the weight and \(x\) the value.
Multiply each value by its weight, add the products, then divide by the total of the weights — not by the number of values.
When to use it
Where components contribute unequally to the overall result.
Examples: exam papers worth different percentages, a price index weighted by how much of each good is bought, or a course grade where coursework and exam count differently.
The common error
Dividing by the number of values instead of the sum of the weights.
If the weights sum to 10 and there are 3 values, dividing by 3 rather than 10 gives an answer more than three times too large. Always divide by \(\sum w\).
Key points
- Each value is multiplied by its weight.
- Weighted mean = sum of wx ÷ sum of w.
- Divide by the total weight, not the count.
- It reflects unequal importance.
- Used for exam papers with different percentages.
- Used for weighted price indices.
Worked examples
Example 1
Two papers score 60 with weight 2 and 80 with weight 3. Work out the weighted mean. [3 marks]
Working
Example 2
Explain why a weighted mean is used rather than an ordinary mean for exam papers of different lengths. [2 marks]
Working
Example 3
Values 10 and 20 have weights 1 and 4. Work out the weighted mean. [3 marks]
Working
Common mistakes
Dividing by the number of values.
Divide by the sum of the weights.
Forgetting to multiply by the weights.
That would give the ordinary mean.
Adding the weights to the values.
The weights multiply the values, they are not added to them.
Using equal weights when the question specifies otherwise.
Read the weights carefully from the question.
Exam tips
- Divide by the sum of the weights every time.
- Show the wx products as a separate step.
- Check the weighted mean lies between the smallest and largest value.
- Remember this is a Higher-only topic.
Key terms
- Weighted mean
- A mean where values are given different importance.
- Weight
- A number showing how much a value counts.
- \(\sum wx\)
- The total of value multiplied by weight.
- Price index
- A weighted measure of price changes.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.