Numerical aptitude · Ratios and averages
Averages, made easy
💡 The idea
The average is what each one would have if everything were shared out equally.
4 · 6 · 8→Total 18→18 ÷ 3 = 6 each
🧭 The method: 3 steps
- Turn averages into totals: total = average × how many.
- Add, take away or fix the totals as the question says.
- Divide the new total by the new count.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
Loading the pictures…
✏️ Worked examples
Example 1. Average of 10, 20, 30 and 40?
- Total = 10 + 20 + 30 + 40 = 100
- 4 numbers → 100 ÷ 4 = 25
Example 2. The average of 5 numbers is 20. A 6th number makes the average 21. What is it?
- Old total = 5 × 20 = 100
- New total = 6 × 21 = 126
- New number = 126 − 100 = 26
⚡ Shortcut: 20 + 1 × 6 = 26 (it gives everyone, itself included, 1 more).
Example 3. The average of 20 marks was 50, but a 64 was entered as 46. Correct average?
- Wrong total = 20 × 50 = 1,000
- Fix it: 1,000 − 46 + 64 = 1,018
- 1,018 ÷ 20 = 50.9
⚠️ Where people go wrong
- The added number is not the new average; it must lift everyone.
- Count again after someone joins or leaves.
📌 Remember
- Average = total ÷ count
- Total = average × count