Weighted average questions and how to get them right

One question of this type, worked in full

Try the question before you read on. The steps take the fastest route that still shows the reasoning, and the last one is the answer the drill marks.

60 customers rated a service a mean of 9 out of 10, and a separate group of 140 customers rated it a mean of 6.5. What is the mean rating across both groups together?

1. Weight each mean by the group behind it: 60 × 9 = 540 rating points.
2. Then the larger group: 140 × 6.5 = 910 points.
3. Add the two totals: 540 + 910 = 1,450 points from 200 customers.
4. Divide by the people, not by the number of groups: 1,450 ÷ 200 = 7.25.

Answer: 7.25 points out of 10. Testonome practice pace: 75 seconds for a question like this.

When the weights are percentages, the method is the same

Some questions give each group's share of the total as a percentage instead of its size. Weight each figure by its share, then add the parts. The five questions in this drill use group sizes, so this example sits here rather than in the set.

Last month 60% of a shop's orders came from its North store, 25% from Central and 15% from South. The mean order value was 45 euros in North, 78 euros in Central and 90 euros in South. What was the mean order value across all three stores?

1. North holds 60% of the orders, so it contributes 60% of 45, which is 27 euros.
2. Central contributes 25% of 78, which is 19.50 euros.
3. South contributes 15% of 90, which is 13.50 euros.
4. Add the three parts: 27 + 19.50 + 13.50 = 60 euros.

Answer: 60 euros.

Four ways this question type goes wrong

Each question offers these alongside the right answer, and the review names which one you took.

• Means averaged

  Averaging the two means as though the groups were the same size.

• Weights swapped

  Attaching each group's size to the other group's mean.

• Larger group only

  Reporting the larger group's mean on its own, so the smaller group never enters it.

• Means added

  Adding the means instead of combining them, which lands outside the scale.

What the review gives you after you submit

You get the working for every question, the answer you chose beside the right one, and the reason the option you picked is wrong. Nothing is sent anywhere while you work.

Other numerical skills you can drill

• Compound growth
• Percentage change