Reverse Mean
Reverse mean (or combined mean) questions are problems that ask for the original set of numbers given the mean (average) of the set.
This type of question is called "reverse" because the usual way to find the mean is to add up the numbers in a set and divide by the number of elements in the set. However, in a reverse mean question, you start with the mean and use it to determine the original set of numbers.
How to solve Reverse Mean Questions
Solving reverse mean questions requires knowledge of mean and the concept of average, as well as the ability to solve mathematical problems using algebraic equations. These questions are commonly found in GCSE mathematics exams and are used to test students' understanding of basic mathematical concepts and problem-solving skills.
Reverse mean questions often involve starting with the mean and working your way back to finding the total. This involves rearranging the formula to calculate the mean. The formula triangles in the picture will prove useful.
Mean = total ÷ how many
Total = mean x how many
How many = total ÷ mean
Reverse Mean Example Question (Edexcel Higher May 2017, Paper 1, Question 7)
Example Question
There are 10 boys and 20 girls in a class.
The class has a test.
The mean mark for all the class is 60
The mean mark for the girls is 54
Work out the mean mark for the boys.
