Weighted Mean
Average where values have different importance.
Key idea
Average where values have different importance.
In depth
When values have different importance, the weighted mean is Σwx/Σw. It generalises the mean and is used for grades, index numbers and combining groups.
Worked example
Exam 80 (weight 60%) and coursework 90 (weight 40%): 0.6 × 80 + 0.4 × 90 = 84.
Formula
Real-world uses
- Calculating a course grade where coursework and exams count differently
- Averaging prices by quantity sold
Common mistake
Averaging group means without weights when groups differ in size.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Weighted Mean?
Average where values have different importance. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Weighted Mean?
The key formula is Σwᵢxᵢ/Σwᵢ.
Where is Weighted Mean used in real life?
Real-world examples: Calculating a course grade where coursework and exams count differently; Averaging prices by quantity sold.
What should I learn before Weighted Mean?
Make sure you are comfortable with Sample vs Population Variance, the previous topic in Probability & Statistics.
What is a common mistake with Weighted Mean?
Averaging group means without weights when groups differ in size.
How can I practise Weighted Mean?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Weighted Mean?
Move on to Percentiles and Z-Scores next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.