What is Reverse Average and Why Should You Care?
Reverse averages are useful when you have the average and one of the contributing values, but the actual number that would complete this average is missing. Whether you are dealing with class grades, financial targets, or sports statistics, understanding reverse averages is an invaluable skill.
How to Calculate Reverse Averages
Here is the formula:
[\text{Missing Number} = 2 \times \text{Average} - \text{Known Number}]
Where:
- Missing Number is the number you are trying to find.
- Average is the overall average you have.
- Known Number is the one number you already know in the set.
Steps:
- Double the average.
- Subtract the known number from this doubled average.
Calculation Example
Given an average of 36 and a known number of 25:
[\text{Missing Number} = 2 \times 36 - 25]
- Step 1: 2 x 36 = 72
- Step 2: 72 - 25 = 47
The missing number is 47.
Another Example
Given an average of 50 and a known number of 30:
[\text{Missing Number} = 2 \times 50 - 30]
- Step 1: 2 x 50 = 100
- Step 2: 100 - 30 = 70
The missing number is 70.