📊 Average - Formula Sheet

🎯 Basic Formulas

Simple Average

Average = (Sum of all values) / (Number of values)

Sum from Average

Sum = Average × Number of values

📈 Weighted Average

Weighted Average = (Sum of weighted values) / (Sum of weights)

Combined Average

Combined Average = (n₁×a₁ + n₂×a₂ + ... + nₙ×aₙ) / (n₁ + n₂ + ... + nₙ)

🔢 Special Cases

Average Speed

Average Speed = (Total Distance) / (Total Time)

When equal distances:

Average Speed = (2 × Speed₁ × Speed₂) / (Speed₁ + Speed₂)

When equal times:

Average Speed = (Speed₁ + Speed₂) / 2

⚡ Quick Calculations

Age Problems

Average age after n years = Current Average + n
Average age n years ago = Current Average - n

Including/Excluding Values

New Average (including) = (Sum + New Value) / (n + 1)
New Average (excluding) = (Sum - Excluded Value) / (n - 1)

📝 Memory Tips

1. Average is always between min and max values
2. Sum = Average × Count
3. For equal spaced numbers, average = middle value
4. Average speed depends on total distance and time

Master Average - Foundation for Data Interpretation! 📊