Averages
Find the mean without adding everything up.
Core Concepts
Instead of adding all numbers and dividing, we use the Assumed Mean Method.
The Deviation Trick
1. Guess an average (e.g., 50).
2. Find how far each number is from your guess (Deviations).
3. Find the average of these deviations.
4. Add this to your guess!
Symmetry Trick
If numbers are equally spaced (like 10, 20, 30, 40, 50), the average is simply the middle number!
Average is 30. No calculation needed!
Solved Examples
Example 1: 42, 45, 48, 50, 55
Question: Find the average.
• Let's assume average is 50.
• Deviations: (42-50)=-8, -5, -2, 0, +5.
• Sum of deviations: -8 -5 -2 + 0 + 5 = -10.
• Average deviation: -10 / 5 = -2.
• Final Average: 50 + (-2) = 48.
Example 2: 22, 24, 26, 28, 30
Question: Find the average.
• These numbers are in an Arithmetic Progression (gap of 2).
• The average is exactly in the middle.
• Middle number is 26.
Example 3: 40, 50, 60, 70
Question: Find the average.
• Gap is 10. Middle is between 50 and 60.
• Halfway is 55.
