Averages
0/10 problems solved
Formulas & 30-Second Shortcut Tricks
Formulas
- Average = Sum / Count
- Average of consecutive numbers = (first + last)/2
- New person replaces one: change in average × n = new − old
Shortcuts
- Deviation method: pick an assumed mean, average the deviations, add back.
- If average of n rises by k when one joins, newcomer = old average + (n+1)k.
Practice problems
The average age of 6 students is 45. When the teacher joins, the average rises by 3. What is the teacher's age?
Find the average of all even numbers from 16 to 34.
The average weight of 10 people rises by 1.5 kg when one person weighing 55 kg is replaced. What is the new person's weight (kg)?
The average age of 10 students is 45. When the teacher joins, the average rises by 4. What is the teacher's age?
Find the average of all even numbers from 22 to 38.
The average weight of 8 people rises by 2 kg when one person weighing 55 kg is replaced. What is the new person's weight (kg)?
The average age of 10 students is 60. When the teacher joins, the average rises by 4. What is the teacher's age?
Find the average of all even numbers from 20 to 50.
The average weight of 8 people rises by 2.5 kg when one person weighing 55 kg is replaced. What is the new person's weight (kg)?
The average age of 8 students is 40. When the teacher joins, the average rises by 2. What is the teacher's age?
Averages Speed Test
1 minute per question. Use the palette to jump around; you'll see time spent on every question at the end.