1. Weighted Means
CCEA GCSE Statistics

2. The Mean
CCEA GCSE Statistics requires knowledge of two methods for calculating the mean:
The Arithmetic Mean
The Weighted Mean

3. The Arithmetic Mean
The Arithmetic Mean is the most commonly used method for calculating the mean
All the numbers in a dataset carry equal weight i.e., they contribute equally to the overall result
Consider the following example:

4. The Weighted Mean The formula for the weighted mean is:
In a Weighted Mean some items of data points may contribute more (or less) to the overall result than others
Consider the same dataset from the previous table but with weights assigned to the individual items of data:
The formula for the weighted mean is:

5. The Weighted Mean Applying the formula for the Weighted Mean:
Assigning greater weight to the larger numbers in the dataset caused the weighted mean (14.6 cm) to be larger than the arithmetic mean (13.4 cm)
Note that the arithmetic mean is equivalent to a weighted mean with equal weights

6. The Weighted Mean
Consider a subject assessed by 1 written exam and 2 controlled assessments (CA); it is easier to get higher scores in the CAs so these are weighted 15% each and the written exam is weighted 70%
A student’s weighted mean result is calculated below:

7. The Weighted Mean
As we can see from the worked example, the result from the written exam carried more weight than the two controlled assessments and this is reflected in the final overall result
Note that the Weighted Index Number seen elsewhere in the CCEA GCSE Statistics course is simply the weighted mean applied to index numbers