Weighted averages in EPSO numerical reasoning
An average across countries, products or groups that do not count equally: an interest rate weighted by debt, a price weighted by customers, a rate weighted by population. It is the family where one single mistake, the plain average, explains the largest share of wrong answers.
7,713 answers, last 60 days · The test gives you 2 minutes per question (10 questions in 20 minutes).
How to recognise it
- What is the average interest rate across the three countries, weighted by their total debt?
- What is the average price per kWh for all customers of Slovakia and Latvia combined?
- What is the overall rate for the four regions together?
The method
- Identify the value to average (rate, price, score) and the weight (debt, customers, population).
- Multiply each value by its weight.
- Add the products.
- Divide by the sum of the weights, not by the number of countries.
Worked example
A question from our bank, in EPSO format.
| Country | Total debt (€ billion) | Average interest rate |
|---|---|---|
| Italy | 600 | 4.0% |
| Spain | 300 | 3.0% |
| Portugal | 100 | 2.0% |
What is the weighted average interest rate on government bonds across the three countries, weighted by their total debt?
Choose an answer to see the solution.
The traps
The simple average
Adding the rates and dividing by the number of countries treats Portugal like Italy. In the example it gives 3.0% instead of 3.5%.
On EPSO Genius, 31% of the wrong answers in this calculation come from this trap.
Dividing by the number of items
After multiplying by the weights, the division is by the total weight (1,000), never by 3.
Weights in different units
If one weight is in thousands and another in millions, convert before multiplying: the heavier item is not always the one with the bigger printed number.
A quick check
A weighted average always lies between the smallest and the largest value, and closer to the item with the biggest weight. 3.5% sits nearer Italy's 4.0%, as it should.
With the EPSO calculator
Write each product on the notepad as you go (2,400 / 900 / 200), then add them. Retyping a long chain in one go is where slips happen.
Practise this calculation
A targeted drill serves only questions of this type, with the full explanation after each answer.
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Frequently asked questions
How do I calculate a weighted average in EPSO numerical reasoning?
Multiply each value by its weight, add the products, and divide by the sum of the weights. Dividing by the number of items gives the simple average, the most common wrong option.
How can I check a weighted average quickly?
It must lie between the smallest and largest values, closer to the item with the largest weight.