Example 1
What is the average of 10, 20 and 30?
- Total = 10 + 20 + 30 = 60
- Average = total ÷ count = 60 ÷ 3
- = 20
Answer: 20
Average Questions with Worked Solutions
Averages explained step by step: the mean of a list, the missing number for a new average and the average of two groups, with worked examples.
How to solve average questions
Average of numbers
Average = the sum of the numbers ÷ how many numbers there are.
Missing number for an average
For the new average m, the total must be m × (count + 1). The missing number is that total minus the sum of the known numbers.
Average of two groups
Weigh each group's average by its size: (n₁ × a₁ + n₂ × a₂) ÷ (n₁ + n₂). The simple mean of the two averages is wrong when the groups differ in size.
Worked examples
Example 2
Three numbers are 10, 12 and 14. What fourth number makes the average of all four numbers 15?
- Total needed for 4 numbers = 15 × 4 = 60
- Total of the known numbers = 10 + 12 + 14 = 36
- Missing number = 60 − 36 = 24
Answer: 24
Example 3
A class has 20 boys with an average mark of 60 and 30 girls with an average mark of 70. What is the average mark of the whole class?
- Total = 20 × 60 + 30 × 70 = 1200 + 2100 = 3300
- Count = 20 + 30 = 50
- Average = 3300 ÷ 50 = 66
Answer: 66