How do you calculate the percentage difference between two numbers?
Understand the Problem
The question is asking how to determine the percentage difference between two numbers. This involves a calculation that compares the difference between the two numbers relative to their average or one of the values, usually resulting in a percentage.
Answer
\left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100
Answer for screen readers
To calculate the percentage difference between two numbers, use the formula: $$ \left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100 $$
Steps to Solve
- Identify the two numbers
Choose the two numbers you want to find the percentage difference between. Let's denote them as $A$ and $B$.
- Calculate the absolute difference between the two numbers
Subtract the smaller number from the larger number to get the absolute difference: $$ ext{Difference} = |A - B| $$
- Calculate the average of the two numbers
Find the average of $A$ and $B$ by adding them together and dividing by 2: $$ ext{Average} = \frac{A + B}{2} $$
- Divide the difference by the average
Divide the absolute difference by the average to get the relative difference: $$ ext{Relative Difference} = \frac{|A - B|}{\frac{A + B}{2}} $$
- Convert to a percentage
Multiply the relative difference by 100 to get the percentage difference: $$ ext{Percentage Difference} = \left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100 $$
Example Calculation
Suppose $A = 40$ and $B = 50$:
- The absolute difference: $$ |40 - 50| = 10 $$
- Calculate the average: $$ \frac{40 + 50}{2} = 45 $$
- Relative difference: $$ \frac{10}{45} \approx 0.2222 $$
- Percentage difference: $$ 0.2222 \times 100 \approx 22.22% $$
To calculate the percentage difference between two numbers, use the formula: $$ \left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100 $$
More Information
Percentage difference provides a way to compare the relative difference between two values as a percentage of their average.
Tips
A common mistake is to forget to use the absolute value when finding the difference. This can lead to negative percentages, which are not meaningful in this context.