Weighted mean (AQA GCSE Statistics): Revision Notes

Weighted mean

What is a weighted mean?

A weighted mean is a type of average where different values have different levels of importance. Instead of treating all data values equally, each value is multiplied by a specific number called a weight that reflects how significant or important that particular value should be in the final calculation.

This is particularly useful in real-world situations where some measurements, scores, or results matter more than others. For example, a final exam might be worth more towards your overall grade than a small homework assignment.

The weighted mean formula

The weighted mean is calculated using this formula:

$\bar{x} = \frac{\sum wx}{\sum w}$

Where:

• $\bar{x}$ represents the weighted mean
• $w$ represents the weight given to each value
• $x$ represents each individual data value
• $\sum wx$ means "multiply each value by its weight, then add all these products together"
• $\sum w$ means "add up all the weights"

Step-by-step method

To calculate a weighted mean, follow these three essential steps:

1. Multiply each data value by its corresponding weight
2. Add up all these products (this gives you $\sum wx$)
3. Divide this total by the sum of all weights ($\sum w$)

Worked example 1: Academic performance

Let's look at how Jim and Anne performed across four different tasks with different weightings.

Even though Jim had higher marks on some individual tasks, Anne achieved a better overall weighted mean because she performed well on Task D, which had the highest weighting.

Worked example 2: Flower show competition

In a flower show, displays are judged on different qualities with different importance levels.

Mr Smith received these marks:

• Shape: 7 (weight = 1)
• Colour: 9 (weight = 2)
• Ambience: 8 (weight = 2)

Notice how colour and ambience have more influence on the final score because they have higher weights.

Worked example 3: Exam percentages

When dealing with percentage marks across different papers, you might need to convert marks to percentages first, then apply the weighted mean formula.

Consider an exam with:

• Paper 1: 52 marks out of 80 possible marks
• Paper 2: 56 marks out of 70 possible marks
• Both papers equally weighted

Key exam tips

Remember!